Although they don't believe in Muhammad (pbuh) as a prophet, they still strongly believe in monotheism and some Jews offer daily prayers (3 times a day if I remember correctly). Islamic and Jewish laws are also very similar. So I think it would be unfair if Allah cast the Jews in hell just because the don't believe in Muhammad (pbuh).
To answer this question we should go through who shouldn't go to Jannah (Paradise) and define some terms.
The ones that are deemed to not enter Jannah are the Kuffar (Kafir). This list could be made longer, but the kafir is the one that is deemed without hesitation.
Now who is a kafir? According to this answer:
A kaffir is somone who disbelives even when they know the truth.
Now, if the person (jew or not) doesn't believe in Islam, not due to pride or not knowing that Islam is the true religion, then that person wouldn't be deemed to be a kafir.
And if that person isn't a kafir, we cannot say that if he dies in that state, that he would go to hell.
How God will judge a person that neither is a muslim or a kafir is only up to Him. He will judge the person with justice. In that case it's fully possible for a jew to enter Jannah.
A person that define a kafir as "non muslim" would of course say that a jew wouldn't enter paradise.
According to orthodox scholars, this matter is pretty clear cut; anyone - and this includes Jews and Christians - who has been made familiar with Islam and does not die a Muslim will go to hell forever according to Islam. As for the verses concerning Jews and Christians whose deeds are accepted, this is thought to refer to those who lived before Islam came, basically as a matter of "god gave them other stuff before, and they followed that, so they are gonna get a reward for that".
One thing that is pretty clear in Islam is that the only question that matters with regard to a verdict of "he will burn in hell forever" is whether or not a person was delivered the message of Islam and accepted it. Muslim scholars are pretty unanimous as far as I can tell in saying that whoever doesn't hear of Islam goes to paradise eventually, and whoever hears of it and doesn't become Muslim, no matter whether he isn't convinced by it, thinks it might be true but so might other religions, doesn't like the rules set by it, or thinks most of it is true but disbelieves, say, in the claim that man was created and did not evolve, will suffer eternal torture for this.
For details see islamqa; some object to islamqa based on it being decidedly salafi, but on this matter, they present the opinion that is shared by the traditional schools of thought of Islam.
Regarding claims that in Islam, no one has authority to say this or that person is fuel for the fire of hell, this is plainly wrong. For one thing, anyone who denies that Abu Lahab is an inhabitant of hell is a kafir; so sometimes there are even quranic verses regarding the fate of particular people. Other than that, islamic theology is very clear on the question of who goes to paradise, and obviously everyone else goes to hell. And finally, jurists after the death of Muhammad have had no problem whatsoever saying someone is in hell if he was judged to have died a disbeliever. Al-Ghazali spends most of his Faysal al-Tafriqa determining what exactly constitutes kufr, and mentions in passing the legal consequences of someone being judged to be a kafir:
Now, all of this is based on the fact that 'Unbelief' is a legal designation (hukm shar'i), like slavery and freedom, its implication being the licitness of shedding the blood of one (sodesignated) and passing a judgement upon him to the effect that he will dwell in Hellfire forever. And since this is a legal designation, it can only be known on the basis of either an explicit text from scripture (nass) or an analogy (qiyas) drawn from an explicit text. Now, there are explicit texts regarding the (status of) Jews and Christians.
In the paragraph preceding that quote, he states
'Unbelief (kufr)' is to deem anything the Prophet brought to be a lie. And 'faith (iman)' is to deem everything he brought to be true. Thus, the Jew and the Christian are Unbelievers because they deny the truthfulness of the Prophet.
Source of both quotes: Sherman Jackson's translation of al-Ghazali's Faysal al-Tafriqa, as found in "Sherman Jackson: On the boundaries of theological tolerance in Islam; p. 92". Note that this is a general statement about all Christians and Jews, which has to be understood with the backdrop that never hearing about Islam will exempt them from hell just like any other kuffar, of course.
On page 115 he elaborates regarding rulings about a specific person, with some basic comment on the standard of proof:
One should not think, incidentally, that either branding a person an Unbeliever or its negation must be based on certainty in every case. On the contrary, 'Unbelief' is a legal designation (hukm shar'i) that refers to 1) a person's loss of property rights; 2) the licitness of shedding his blood; and 3) his dwelling in the Hellfire forever. As such the basis upon which it is established is the same as that upon which the rest of the rules of the religious law are established: sometimes they are based on certainty; sometimes on preponderance of probability; and sometimes on sources to which one cannot fully commit either way.
It should be very clear from this that it is a perfectly accepted practice to call someone an inhabitant of hell if the shar'i preconditions are fulfilled, i.e. if someone being a kafir is sufficiently evident. The question who has the authority to pronounce such a judgement is a different one, but it definitely is not "only god" and clearly includes the judge in a case where someone's status as being a kafir or not is relevant.
I acknowledge that the stance of "we don't judge anyone" is popular among muslims, but it has no grounding in orthodoxy. In fact, al-Ghazali finishes Faysal al-Tafriqa by addressing exactly that position:
There are some who say, 'I simply brand as Unbelievers those groups who brand me an Unbeliever. Those who do not brand me an Unbeliever, I do not brand them so.' This position, however, is unfounded.
For were someone to say, 'Ali, may God be pleased with him, is most qualified to be Imam, assuming that he was not an Unbeliever,' then wrongly hold the latter [i.e. Ali, my comment] to be an Unbeliever, though we hold to be an Unbeliever anyone who (on purely ideological grounds) challenges Ali's status (as an upright Companion), this person would not be so condemned, because his position would simply constitute an error (in his factual assessment) regarding a religiously relevant question. Similarly, if the Hanbalite is not deemed an Unbeliever because he holds God to be located in a specific direction, he cannot be branded an Unbeliever because he thinks or mistakenly holds those who deny God's being located in a specific direction to be guilty of deeming (the Prophet) to be a liar rather than being engaged in (legitimate) figurative interpretation.
As for the statement of the Prophet, 'Whenever a Muslim charges his fellow Muslim with Unbelief, this redounds upon one of them,' this refers to instances where he brands him an Unbeliever with full knowledge of his true state. In other words, if a person knows that another person believes that everything the Prophet brought is true and despite this he brands the latter an unbeliever, he becomes himself an Unbeliever. As for his branding this person an Unbeliever because he sincerely thinks that the latter holds the Prophet to be a liar, this is simply a mistake on his part regarding this particular individual. For he may think that this person is indeed an Unbeliever who holds the Prophet to be a liar, while in fact this is not the case. This, however, does not constitute an act of Unbelief.
Source: "Sherman Jackson: On the boundaries of theological tolerance in Islam; pp. 131, 132". The point of this paragraph to me seems to be that calling someone an Unbeliever when you truly think he is an Unbeliever does not constitute an act of Unbelief, i.e. kufr, which is one of the common objections to doing so. Put differently, al-Ghazali defends the act of calling someone an Unbeliever if you truly think he is an Unbeliever. As we have seen, a judge deeming someone a kafir is a legal judgement that also concerns their status in the islamic hereafter.
Disclaimer: I am not a muslim.
Not only them buy anyone who believes as such:
إِنَّ الَّذِينَ آمَنُوا وَالَّذِينَ هَادُوا وَالنَّصَارَىٰ وَالصَّابِئِينَ مَنْ آمَنَ بِاللَّهِ وَالْيَوْمِ الْآخِرِ وَعَمِلَ صَالِحًا فَلَهُمْ أَجْرُهُمْ عِندَ رَبِّهِمْ وَلَا خَوْفٌ عَلَيْهِمْ وَلَا هُمْ يَحْزَنُونَ
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.
Chapter Baqara, verse 62: