Depending on how the cookie crumbles for the Bajoran government, the Federation might end up with a substantial refugee crisis. They then do their best to provide humanitarian aid to the maximum extent their laws allow.And, in this example, every Bajoran who did not agree with the unconstituonal theocracy is going to rightfully demand from the Federation protection from local despotism.
It is, however, naive and arrogant to think the Federation has a responsibility to play superman and impose order on the rest of the universe. This line of thinking very quickly devolves into Dominion style imperialism.
That depends. Is the mob in control of the government or just the military?Is it correct to abandon the billions-strong minority of Federation citizens who are going to have the right to life--that the Federation promised to provide them upon admission--stripped away by a theocratic mob?