What is the ruling on praying behind an Imam who believes in democracy and advocates gradual implementation of Allah's law?

Democracy is a new term, previously unknown to Muslims. No judgment can be passed on it except by clarifying its intended meaning. If it refers to Shura (consultation), then it is acceptable, though it is preferable to use the religiously prescribed term. However, if it means that the people are the source of legislation, then it is void and constitutes disbelief (kufr), because legislation is a right belonging to Allah alone. Whoever claims that democracy is permissible in this sense must be advised.

As for gradual implementation of Sharia: If it means implementing what is possible and striving to gain the ability to implement the rest, then it is correct. However, if it means abandoning what can be implemented of the Sharia's rulings without detriment, then it is void.

In general, it is not permissible to rush into judging people before clarifying the matter, and praying behind every Muslim is permissible unless it becomes clear what would exclude them from the Ummah.