What line of argument do the Ahlul Sunnah use to support the belief that Abu Talib (ra) died as a disbeliever? How do the Shi'a respond to it?
Sunni view:
(a) He never openly converted
(b) Some quotations from Sunni hadith and history books and interpretations of Qur'an.
Shi'i view:
(a) He was obviously a clear supporter of the Prophet and couldn't have done that if he were openly a Muslim.
(b) Hadith and quotations such as the marriage khutbah he is said to have recited for the Prophet (S) and Khadijah
In my view, the important thing is to maintain respect for him as a human being and not make this into a purely sectarian issue. Often, certain issues are hotly debated between Sunnis and Shi'is not for their own sake, but because they are closet debates aiming to prove "I'm right and you're wrong", which is more about ego or group identity than the actual issue at hand.
Further details can found rather copiously online!