I think occasionally it needs to be in the focal point, especilly when we have such issues around it still, but on going you just need to feed characters in where normally it would be a straight person/couple. I.e. you could swap them round and it would be th esame and actual sexuality isn't even mentioned. Essentially that's the highest stage and where people really want to see it.
But the idea of LGBT refugees is good, though TOS usually did it in metaphors. I think TNG had that third gender episode which was as close as mainstream Trek ever got to addressing sexuality. How about taking inter-species love but dressing the issues said group or couple facing entirely in the ways and language the gay community has been attacked?
One of the problems I see is that to do a proper metaphor with LGBT rights, at some point you need to look at religion. It's very sensative and I'm worried about the T&C on foundry.