It's pretty true that his running mate has a rather sour history in regards to the LGBT community, as does the GOP as a whole - who just happen to have majorities in both houses of congress at this moment.
None of this has anything to do with Trump himself, of course, and the GOP majorities in congress aren't significant enough to forcibly pass any sort of anti-LGBT legislation should Trump veto them - but that assumes he would actually do so. It's also possible for discriminatory laws to be implemented at the state level, so I'm curious whether he would have some sort of response to that or if he would just leave it up to the states.
I'm personally more concerned about his previous talking points of preventing immigration based on religious affiliation, as well as a number of his other more-questionable stances in regards to personal liberties. Given that he's publicly said he supports stop and frisk, said he wants surveillance of mosques, indicated that he wishes to get Roe v Wade overturned, and wants to restore provisions of the patriot act, it's pretty clear he tends to value security and what the GOP likes to call family values over personal liberty - at least publicly. But then again, maybe Hillary's snippet about public and private positions applies to Trump as well
Regardless, the US survived 8 years of Bush. I think all that matters is that people just do them, make the best of it, and the US will truck on as usual. I think it's important to remember that every last man that voted Trump is a fellow American, as is every last one that voted Hillary.