How can a Muslim act in condolence gatherings that include the communal recitation of Al-Fatiha, offering hospitality, and exchanging customary condolences, while knowing that these practices may be considered innovations, and at the same time not wishing to sever family ties or be accused of extremism?

There is nothing specific regarding offering condolences. Donating the reward of reciting the Quran to the deceased is permissible. Sitting to receive condolences is considered disliked by a group of scholars, though it is acceptable out of necessity. It is important to invite people and guide them by explaining the rulings of Islamic law concerning these actions, while being gentle with them, treating them kindly, and maintaining kinship ties.