Inspired by the Churva Synagogue of R. Yehuda HaChassid (18th cent.) who was likely a Sabbatean (not to be confused with the 12th century rabbi of the same name), and his congregation which almost certainly included Sabbateans, I ask whether it is permitted to pray in a Sabbatean synagogue.
This in light of the fact that Sabbatean ideology included seemingly idolatrous elements.
I recognize that the Churva Synagogue in particular has been destroyed (hence the name) and subsequently rebuilt, and thus likely lost whatever its original legal status was. However, this was just the inspiration for the question. The question is not asking about the Churva in particular, but rather about Sabbatan sites in general.