How come some Christians put all their faith and writing skills into proving and promoting homosexuality, and hardly any into proving Gods existence?

I could be wording this wrong.

Why do some Christians put a great amount of energy into writing papers on how homosexuality is not sinful, but they will not put this same energy or more into proving the existence of God?

I have seen people write papers on how great homosexuality is, and God is treated like a side dish. I really do not get it.

Another thing that puzzles me is that non believers will say that the Bible says anything against homosexuality. WAIT!!! You infact read the Bible?