The phrase "to fit in with" means to be compatible or suitable for a particular situation, group or environment. It refers to adapting one's behavior, beliefs, values or characteristics to blend in and harmonize with others around them.
If what we discover doesn't fit in with what evolution predicts then evolution is wrong. (religion.blogs.cnn.com)
People are usually afraid of something new that doesn't fit in with what we have been told to be the «truth» and therefore have believed in. (nakedpastor.com)
I will explain how a book fits in with other books of the bible by grouping the books. (dailyfreebooks.com)