I don't really care if he changes his opinion or not; I have an issue with people who go out of their way to prevent other people from having something when it loses them nothing.
If there was any sort of reason why banning gay marriage was economically beneficial or caused tangible harm to any group of people, then it would be 'live and let live', but at some point, he decided to attempt to prevent gay people from getting married for no reason other than what effectively comes down to spite. That's not really someone I trust in a leadership position.