If one is a Christian or another religion of the books, sincerely believes in God, and refrains from the sins of his religion. Will this person be able to go to heaven?

مَنْ عَمِلَ صَالِحًا مِّن ذَكَرٍ أَوْ أُنثَىٰ وَهُوَ مُؤْمِنٌ فَلَنُحْيِيَنَّهُ حَيَاةً طَيِّبَةً وَلَنَجْزِيَنَّهُمْ أَجْرَهُم بِأَحْسَنِ مَا كَانُوا يَعْمَلُونَ

As for anyone – be it man or woman – who does righteous deeds, and is a believer most certainly We shall cause him to live a good life. and most certainly shall We grant unto such as these their reward in accordance with the best that they ever did