It's not about liking gays. It's not about his personal morals influencing decisions. It's about inconsistency.
Your partisan video takes snippets of speaches he made left and right out of context, so of course it looks inconsistent, that's what the editor of the video intended.
Yes he is a Christian, and yes his religion influences his policies, but he's also American and he knows this has its limits, and he will run into opposition if he goes too far.
Again, not very extraordinary.