Is it permissible for a mosque that seeks to be among Ahl As-Sunnah wal Jama'ah to pray the Eid prayer with a Sufi mosque that believes the Messenger of Allah and the deceased come to them in a waking state, and a third mosque run by Ash'aris, knowing that they will lead the prayer?

One should not pray behind innovators (Ahl al-Bid'ah) if there are others available from Ahl al-Sunnah. The prayer of an individual behind them is valid, though disliked (makruh). However, the reward for his prayer may be diminished. This is provided that the innovation or disobedience of the Imam does not reach the level of disbelief (kufr); otherwise, his prayer and following him are not valid.