Will God punish people for not being Muslim? If they ask for forgiveness, repent, and never repeat the same sins will they still be sent to hell for not being Islamic? Or if they refrain from drinking alcohol and give to charity, will they be sent to hell for not becoming a muslim?
(My answer is with regard to the question "who goes to suffer in hell forever", since going to hell for a finite time is eventually irrelevant, and very simple: anyone who sins might go there for a finite time, muslim or no.)
The matter is pretty clear cut in sunni islam on this absolutely fundamental question. While it is true that islam teaches no one can see into hearts which one would have to to be able to to judge a person, it is also true that islam is very clear on how the judgement will be made.
The judgement for anyone who is delivered the message sufficiently and is not completely convinced by the central tenets of islam - Qu'ran being the unaltered and literal revelation of the one god Allah, Muhammad being god's last and truthful messenger, and the Last Day - and dies without completely accepting these claims as true is considered a kafir who is condemned to suffering in hell forever. His deeds do not matter, what he did and believed before the moment of his death does not matter.
This is the completely dominant position, and only very few ever tried to argue for potential salvation of such a person - among them ibn Arabi, who said the people in hell will come to enjoy being there, and ibn Taymiyyah, who said hell must eventually extinguish. Both of their opinions on this matter have been rejected by almost all scholars, and a few even declared those opinions kufr, if I remember correctly.
There are some exceptions, and I will list them here.
- The first are Jews and Christians before Muhammad - anyone in this category has been dead for more than a thousand years.
- The second are people who never learn islam sufficiently out of lack of opportunity, but I have seen very little discussion of what qualifies as "sufficiently"; usually when I see talk about this, the conclusion is that learning the central tenets of islam as they actually are in islam and a more or less summary biography of Muhammad will suffice. Some scholars - perhaps most, I'm not sure here - say there will be a test for those people on judgement day. They will be ordered to step into fire to be granted entry to paradise; those who step into it will find it to be cool and pass the test, and those who refuse will be dragged to hell for their disobedience.
- The third exception are people of poor mental health, children, basically people who do not reach a state of mind where they are adult and sane enough to evaluate the claims of islam.
- A fourth group, listed by very few I have seen, is Allah just forgiving someone on judgement day - the reason this is usually not mentioned is because it goes against the quranic statement that god will not forgive shirk.
Al-Ghazali in faysal at-tafriqa (available in a translation by Prof. Sherman Abdulhakim Jackson) is explicit on these matters. Muhammad Hassan Khalil in his Ph.D. thesis catalogues the views of ibn Arabi, al-Ghazali, and ibn Taymiyyah (alongside the probably heterodox Muhammad Rashid Rida) regarding the fate of "the other", i.e. non-muslims, and contains numerous references. It is explicit that almost without fail, sunni scholars say precisely what I summarised above - and the express purpose of the thesis is to look for scholars who have authority in the sunni tradition and disagree with what I wrote above, and concludes that the views of ibn Arabi and ibn Taymiyyah have been rejected by almost all scholars and some even declared their views kufr. For details check the references there. IslamQA is explicit that the fate of a kafir who hears of islam is eternal suffering in hell, and that the sole reason for eternal punishment is non-acceptance of islam. Hamza Yusuf in Who are the Disbelievers reiterates and ruminates on this position.
TL;DR: This is up to Allah. We can surmise some things based on what's in the Qur'an and ahadith, but there's a lot of exceptions (detailed below). Not even a devout Muslim can feel secure not to enter hell.
A relevant ayah here is:
Indeed, those who believed and those who were Jews or Christians or Sabeans [before Prophet Muhammad] - those [among them] who believed in Allah and the Last Day and did righteousness - will have their reward with their Lord, and no fear will there be concerning them, nor will they grieve. -- Qur'an 2:62
but this is not as straightforward as it first sounds:
The verse, as mistakenly understood, does not signify that belief in God and in the Last Day alone is sufficient for salvation. The Qur'an emphatically declares that belief in the Holy Prophet is most essential [Qur'an 4:150-151; Qur'an 6:92] and forms an integral part of belief in God, and also that belief in the Hereafter includes belief in Divine revelation as well. -- Malik Ghulam Farid (ed.), The Holy Qur'an (Arabic Text with English Translation & Short Commentary), 2003 (first published 1969), p. 36.
which is also not as straightforward as it sounds:
The verse [Qur'an 2:62] may also be taken as signifying that all those who claim to be believers whether they are Jews, Christians, or Sabians, or, for that matter, belong to any religion---if their faith in God and the Last Day is sincere and honest and they do good deeds which is the quintessence of a true religion, i.e., Islam, no fear shall come upon them nor shall they grieve. -- Farid op. cit.
The Qur'an often talks about who is going to hell: Qur'an 2:62; Qur'an 2:165-167; Qur'an 4:168-169; Qur'an 6:44; Qur'an 6:128; Qur'an 7:40; Qur'an 11:106-107; Qur'an 18:2; 33:64-65; Qur'an 35:36; Qur'an 43:74-75; Qur'an 64:10; Qur'an 72:23. (I'm not sure if this is a complete list; it probably isn't.)
From this list of ayat, it is clear that disbelief and shirk is the main reason that people end up in hell, and (unsurprisingly) scholars believe what it says in the Qur'an:
However, there is a significant amount of nuance to this:
Who goes to hell is up to Allah's judgement. As such, it's generally improper for Muslims to declare who is or isn't going to hell.
And [mention, O Muhammad], the Day when He will gather them together [and say], "O company of jinn, you have [misled] many of mankind." And their allies among mankind will say, "Our Lord, some of us made use of others, and we have [now] reached our term, which you appointed for us." He will say, "The Fire is your residence, wherein you will abide eternally, except for what Allah wills. Indeed, your Lord is Wise and Knowing." -- Qur'an 6:128
As for those who were [destined to be] wretched, they will be in the Fire. For them therein is [violent] exhaling and inhaling. [They will be] abiding therein as long as the heavens and the earth endure, except what your Lord should will. Indeed, your Lord is an effecter of what He intends. -- Qur'an 11:106-107
Respected brother in Islam, the Realms of Paradise is the prerogative of Allah Subhanah Alone; and the two absolutely inseparable pre-conditions the Lord Most High Most Wise has conveyed in His Message for ones entry into the Eternal Gardens of Paradise are: 1. Belief, and 2. Righteous good deeds in accordance with the Guidance of the Lord. -- Islam Helpline
They, like other sinners among the monotheists, will be subject to the will of Allah, may He be glorified and exalted: if He wills, He will punish them, and if He wills, He will forgive them, then the final destination of any one of them will be Paradise, if he died believing in Tawheed. -- Islam Q&A fatwa
The enormity of that judgment on a person is so great that it is legally prohibited to say that anyone is destined for the Hellfire unless a clear verse or a hadith with multiple transmissions indicates such. -- Hamza Yusuf, Who Are the Disbelievers? (pdf)
Being a Muslim does not mean you're exempt from hell, but it helps.
Not only unbelievers, but many Muslims will enter the Hellfire. However, the believers who enter Hell due to their sins will ultimately be taken out after their term of punishment is completed and they will be admitted to Paradise. -- IslamToday fatwa 1315
None shall enter the Fire (of Hell) who has in his heart the weight of a mustard seed of Iman and none shall enter Paradise who has in his heart the weight of a mustard seed of pride. -- narrated on the authority of 'Abdullah b. Mas'ud (sunnah.com)
Some people who enter hell are taken out.
I will say, 'O Lord, my followers! My followers!' And then it will be said, 'Go and take out of Hell (Fire) all those who have faith in their hearts, equal to the weight of a barley grain.' I will go and do so and return to praise Him with the same praises, and fall down (prostrate) before Him. -- Narrated Ma`bad bin Hilal Al-'Anzi (sunnah.com)
...There are many sound Ahadeeth that prove that anyone who has a part of an atom of belief in Allaah, he will not stay eternally in Hell -- Ibn Katheer (sourced from IslamWeb fatwa)
Ultimately, God will remove from Hell those believers whose sins were not forgiven nor atoned for by good deeds in their lifetimes, and they will then enter Paradise. The remaining inhabitants of Hell will stay there eternally. (attributed to IslamOnline.net by ReligionFacts)
Khalil summarises the Ibn Taymiyyah's arguments in favor of this distinction, one such argument being:
"...it has been established that God will allow into Heaven... people who were initially consigned to Hell..." -- Mohammad Hassan Khalil, Muslim scholarly discussions on salvation and the fate of others, PhD thesis, 2007 (pdf)
It's even argued that hell will become empty over time:
This view, which Ibn Taymiyyah goes to great lengths to support, entails that the punishment in Hell will eventually cease to exist, and that everyone will leave it at some point. This, it is argued, is a viewpoint that has been conveyed on the authority of Companions such as 'Umar ibn al-Khattab, Ibn Masud, Abu Hurayrah, Abu Said al-Khudri, and others. -- Khalil (op. cit.)
Hell has multiple "levels", some worse than others:
Allah is forgiving, except of shirk:
Indeed, Allah does not forgive association with Him, but He forgives what is less than that for whom He wills. And he who associates others with Allah has certainly fabricated a tremendous sin. Qur'an 4:48
And there is also a matter of intercession:
Surely Allah wrongs not the weight of an atom; and if it is a good deed. He multiplies it and gives from Himself a great reward" (al-Qur'an, iv. 40). Then Allah, Exalted and Great, would say: The angels have interceded, the apostles have interceded and the believers have interceded, and no one remains (to grant pardon) but the Most Merciful of the mercifuls. He will then take a handful from Fire and bring out from it people who never did any good and who had been turned into charcoal, and will cast them into a river called the river of life, on the outskirts of Paradise. (sunnah.com)
Even going to hell for disbelief is nuanced:
This does not negate the legal status of those who believe in the trinity as kafirun but rather suspends judgment on their intention since many of them may be unaware that they are in a state of blasphemy. -- Hamza Yusuf, Who Are the Disbelievers? (pdf)
There's a kind of indirect disbelief, where disbelief in God can be inferred by disbelief in that which He has decreed.
...in al-Ghazali's theological treatis al-Iqtisad fi al-i'tiqad (The Middle Path in Belief), he states point-blank that whoever denies (the prophethood and messengership of Muhammad is an Unbeliever (kafir) and will remain (mukhallad) in Hell `forever' ('ala al-ta'bid). -- Khalil (op. cit.)
(Khalil also writes: "...al-Ghazali's writings appear to be at least partly geared towards assisting fellow Believers in their quest for salvation, and possibly guiding 'sincere' non-Muslims who are not true Unbelievers.")
the first condition to avoid being thrown in Hell-Fire is to have a true belief in Allah and in His Angels and in His Books and in His Prophets and in The Last Day and in Predestination, good or bad. So anybody who does not firmly believe in the above has no chance of avoiding Hell-Fire. Indeed, this true belief (Iman) is a precondition to the acceptance of the good deeds. So, the unbelievers who do some good deeds in this life are rewarded in this life by more comfort, … etc. But they do not deserve any reward on the Day of Judgement. -- IslamWeb fatwa
It could be argued that someone who never converts to Islam is a disbeliever (i.e., they don't truly believe in God).
So my answer to Do people who never convert to islam still go to hell even if they believe in God? is:
I don't know; the decision is up to Allah (point 1). In fact, I can't even be certain that I'm not going to hell, and I'm a Muslim striving not to sin (point 2).
The Qur'an affirms that clear-cut instances of disbelief and shirk land people in hell. Aside from that, it's complicated and debated. (How long does one spend in hell? [point 3-4] Which level of hell does one go to? [point 5])
There's probably not a simple yes/no answer to this question (points 6-8).
It depends on what is meant by "converting to Islam" and "believing in God" [point 9]. How can one truly believe in God, but reject what God says?
One possibility is that they are People of the Book, ("...our God and your God is one..." -- Qur'an 29:46), which is this question: Do non-Muslims have a chance to go to Paradise? Even this is nuanced, as per Farid op. cit.
No one can answer you this question, Quran has clarified this clearly in many verses. Please read.
Indeed, the religion in the sight of Allah is Islam. And those who were given the Scripture did not differ except after knowledge had come to them – out of jealous animosity between themselves. And whoever disbelieves in the verses of Allah , then indeed, Allah is swift in [taking] account.
In another text
And whoever desires other than Islam as religion - never will it be accepted from him and he in the Hereafter will be among the losers
The texts explain themselves. Now the question is how to be a muslim?
The main things you need to do as a muslim
- To do the testimonies: there is no god but allah, and mohammad is his messenger. This is the main belief of islam
- To pray
- To pay the Zakat (Zakah)
- Pilgrimage (only those who can)