I've gone out with a ton of people and have only had this type of rejection experience once, with someone who had a lot of childhood bullying trauma so it really wasn't about me in retrospect. And publicly disclosing doesn't seem to have affected people's interest.
The things I can say are that apart from living in a liberal area and looking like a cis woman is that I've come to a point when I really don't need a guy to accept it and the men I meet can sense that. Post-transition, it's really important to get over this no one is ever going to love me feeling because that's precisely what alienates potential lovers, the idea that you're just with them because you're desperate rather than you actually appreciating them for who they are. I dislike it when other people make me feel that way so same goes the other way around.
Oddly enough, I think Facebook and being out helps in this regard in the sense that men who are interested in me see other, seemingly normal, professional, intelligent guys on my Facebook who are exes, good friends, etc. So the whole idea of potentially dating a trans woman becomes more normal to them, and they also know that I might move on if they don't take the chance. So for me, being out has actually led to more rather than fewer opportunities. I totally adore my boyfriend and am quite loyal to him, but we're non-exclusive so I like having cute boys around to flirt with!