Well, Fagin was a thief as well as a fence, in the book, the film and the stage musical. Training kids to carry out the legwork and the fingerwork involved in stealing is a variety of theft.

But he doesn't need to have convinced himself that he is honest in order to be religiously observant. Just that he is doing what he has been forced to do by circumstances, maybe that what he has done is not that bad, and that he is an imperfect human being who can pray to be forgiven before it's too late.