I would like to quote two verses from the Holy Quran
يَا أَيُّهَا الَّذِينَ آمَنُواْ اتَّقُواْ اللّهَ وَابْتَغُواْ إِلَيهِ الْوَسِيلَةَ وَجَاهِدُواْ فِي سَبِيلِهِ لَعَلَّكُمْ تُفْلِحُونَ
O ye who believe! Be mindful of your duty to Allah, and seek the way of approach unto Him, and strive in His way in order that ye may succeed.(5:35)
In this verse Allah (s.w.t.) tells the believer to reach the level of takwa and piety. It should be noted that takwa is a higher level of faith when a person tries to abstain not only from the Haram acts but also from the Makrooh ones. He tries to perform not only the compulsory ones but also tries to perform the Mustahab ones.
Every believer might not be a muttaqi but every muttaqi has to be a believer.
وَمَا لَهُمْ أَلاَّ يُعَذِّبَهُمُ اللّهُ وَهُمْ يَصُدُّونَ عَنِ الْمَسْجِدِ الْحَرَامِ وَمَا كَانُواْ أَوْلِيَاءهُ إِنْ أَوْلِيَآؤُهُ إِلاَّ الْمُتَّقُونَ وَلَـكِنَّ أَكْثَرَهُمْ لاَ يَعْلَمُونَ
But what plea have they that Allah should not punish them, when they keep out (men) from the sacred Mosque - and they are not its guardians? No men can be its guardians except the righteous; but most of them do not understand.(8:34)
In the above verse Allah (s.w.t.) says that none can be the guardian of the Holy House except the righteous. (ie except the Muttaqi)
Now, its an undisputed historical fact that Hazrat Abu Talib (as) was the guardian and the caretaker of the Holy House. Relating both the verses of the Quran we come to the conclusion that Hazrat Abu Talib (as) was not only a believer but his faith was of a higher lever then ordinary people.
And when Allah (s.w.t.) calls comebody a pious one then questioning his belief is questioning the words of Allah (s.w.t.) and any body who questions the words of Allah (s.w.t.) is a Kafir.
One point which I would like to quote over here is that a rightful caretaker of the House Of Allah (s.w.t.) would only be the one who is appointed by Allah (s.w.t.) himself, and not those who have usurped the rights of the rightful owners as is the case today.