Is it permissible to pray behind imams of a Sufi mosque who declare supplication aloud after every prayer and intercede through the Prophet, may Allah bless him and grant him peace, in private gatherings?

The congregants of the mosque raising their voices in supplication after prayer does not necessarily make them Sufis. It could be due to ignorance or imitation. However, their private gatherings and their seeking intercession through the Prophet (peace be upon him) strengthen this assumption. Intercession through the Prophet (peace be upon him) is of two types: The first is major shirk (polytheism), which is supplicating to him and seeking his help. The second is an innovation (bid'ah), which is seeking intercession through his status (jah) or his right (haqq). They should be gently taught. If they do not respond, then praying behind them is valid and preferable to abandoning congregational prayer, especially if no other mosque is available. If their innovation is polytheistic (shirkiyyah), then praying behind them is not valid. However, if it is not polytheistic, such as some forms of dhikr, then the prayer is valid, but it is better to pray behind an imam who is not an innovator.