sunni
The sunnis generally hold that he died as a disbeliever, disagreement on this among them is uncommon. The reports on this are reliable according to the criterion of the sunnis.
The following three hadith are collected together by Bukhari in the chapter on Abu Talib:
حتى قال أبو طالب آخر ما كلمهم على ملة عبد المطلب، وأبى أن يقول لا إله إلا الله. قال قال رسول الله صلى الله عليه وسلم والله لأستغفرن لك ما لم أنه عنك ". فأنزل الله {ما كان للنبي والذين آمنوا أن يستغفروا للمشركين} وأنزل الله في أبي طالب، فقال لرسول الله صلى الله عليه وسلم {إنك لا تهدي من أحببت ولكن الله يهدي من يشاء}
Till Abu Talib said as the last thing he said to them, "I am on the religion of `Abdul Muttalib," and refused to say: None has the right to be worshipped except Allah. On that Allah's Messenger (ﷺ) said, "By Allah, I will keep on asking Allah's forgiveness for you unless I am forbidden (by Allah) to do so." So Allah revealed:--
'It is not for the Prophet and those who have believed to ask forgiveness for the polytheists, even if they were relatives, after it has become clear to them that they are companions of Hellfire.' (9:113)
And then Allah revealed especially about Abu Talib:--
'Verily! You (O, Muhammad) guide not whom you like, but Allah guides whom He will.' (28:56)
— Bukhari
This report states that Abu Talib refused to say the shahadah and that the above verses in the Quran were revealed about him, which declare him to be a Mushrik and not guided.
حدثنا العباس بن عبد المطلب ـ رضى الله عنه ـ قال للنبي صلى الله عليه وسلم ما أغنيت عن عمك فإنه كان يحوطك ويغضب لك. قال هو في ضحضاح من نار، ولولا أنا لكان في الدرك الأسفل من النار
Narrated Al-Abbas bin `Abdul Muttalib:
That he said to the Prophet (ﷺ) "You have not been of any avail to your uncle (Abu Talib) (though) by Allah, he used to protect you and used to become angry on your behalf." The Prophet (ﷺ) said, "He is in a shallow fire, and had It not been for me, he would have been in the bottom of the (Hell) Fire."
— Bukhari
عن أبي سعيد الخدري ـ رضى الله عنه ـ أنه سمع النبي صلى الله عليه وسلم وذكر عنده عمه فقال لعله تنفعه شفاعتي يوم القيامة، فيجعل في ضحضاح من النار، يبلغ كعبيه، يغلي منه دماغه
Narrated Abu Sa`id Al-Khudri:
That he heard the Prophet (ﷺ) when somebody mentioned his uncle (i.e. Abu Talib), saying, "Perhaps my intercession will be helpful to him on the Day of Resurrection so that he may be put in a shallow fire reaching only up to his ankles. His brain will boil from it."
— Bukhari
Being in hell is an indicator that he died on disbelief.
The following hadith is also used:
عن أسامة بن زيد، أنه قال زمن الفتح يا رسول الله، أين تنزل غدا قال النبي صلى الله عليه وسلم وهل ترك لنا عقيل من منزل . ثم قال لا يرث المؤمن الكافر، ولا يرث الكافر المؤمن
Usama bin Zaid said during the Conquest (of Mecca), "O Allah's Messenger (ﷺ)! Where will we encamp tomorrow?" The Prophet (ﷺ) said, "But has `Aqil left for us any house to lodge in?" He then added, "No believer will inherit an infidel's property, and no infidel will inherit the property of a believer."
— Bukhari and Muslim
If Abu Talib was a Muslim then by Islamic law his property would have gone to Ali and Jaffar (who were Muslims) and not to Aqeel (who was not Muslim at that time).