What specific protections that actually fall under the Executive's unilateral authority are you looking for? The Presidency isn't a kingship, and the federal government's authority to interfere with state laws is limited, particularly in the absence of a friendly Congress.
Re: Housing, discrimination based on gender identity or sexual orientation is illegal and you can file a complaint with the Department of Housing and Urban Development if you experience it.
Harassment is, for better or for worse, a pretty high bar, and the President absolutely does not have the power to prevent people from being assholes to us. If healthcare is in reference to HRT, the administration has been heavily involved in pushing back against state laws, but again, there are constitutional constraints.
That aside, I like to think that the Pride flag flying at embassies is a very nice signal of what America can stand for at its best, particularly in countries where LGBT people won't otherwise see any kind of support at all. It's obviously not the same thing, but as a gay kid from a tiny rural southern town, it was always cool when I traveled to cities and saw Pride flags or saw Pride campaigns on TV as a way to know that not everyone was like my hometown.