I'm curious why a question like this is even asked. How in any way would his belief if it's a choice to be gay (which its obviously not) affect his ability to run the country. I wish we could actually talk about the issues for once.
Here is why. If you believe being gay is a choice, then gay people should be treated like model train enthusiasts. You have nothing against them and they have every right to enjoy their 'lifestyle' but they shouldn't have any 'special protections.' Whereas if you believe it isn't a choice, then sexual orientation becomes like race/ethnicity. And therefore deserves protection from discrimination.
I take the Biblical view of homosexuality. That being said, the goal of homosexuals has been to become a protected minority, regardless of the lack of proof that homosexuals are "born that way". They've just about achieved that goal when the SSM ship sailed.
"Sexual orientation" is going to be like race and ethnicity in the next few years. And it won't matter if it's a Democratic or Republican President; the Courts will end up doing this. There's legal precedent for this now. And the moral compass of America is such that there are more that 13 states that would block any Constitutional Amendment to undo
Obergefell.
This is, I believe, an issue that the GOP wants to go away, and fast.