You can't think of any sci-fi that CAN contain relevant LGBT elements to it? Well, for ones that actually do, tehre's some big Wikipedia list I don't have time to get through, so here.
https://en.wikipedia.org/wiki/List_of_LGBT-themed_speculative_fiction
But in regard to actual usage, it's not very hard. You can go straightforward and directly have them deal with LGBT issues. I can think of an abundance of sci-fi pieces that deal with the concept of both sex and gender being radically different for alien species, dealing with a discussion of the difference between sex and gender, but you can also go with whatever forced homosexuality or heterosexuality Clamurai mentioned.
Of course, the cooler way to deal with it is through metaphor. At its thinnest, Futurama had an episode that deal with robot-human marriage, and was clearly meant to be a metaphor for homosexual marriage. Of course, you can take it to any place you want to with this.
Maybe you try to make a point about how trans people are marginalized, you write a story a story about an alien without gender struggling to fit into Terran society, and just keeping reaching issues as humans expect it to adhere to their idea of gender, and casually just kind of push it into that role.
Maybe cloning becomes popular, but clones are seen as sort of these lesser people, and there's an outbreak of disease among them because they're cloned, but it's hinted its mainly because they don't have same access to healthcare, for a good whole analogy about gay life and dealing with AIDS in a toxic society.
Maybe it's about an AI that wants to reproduce, but AI reproduction is illegal due to fears of a singularity, so the AI wants to adopt biological children, but people say that you can't raise a child without biological parents, and that a human child needs a human mother, and it's all a big analogy for gay adoption.
There's endless ways you can use sci-fi to talk about LGBT+ issues, it's only restricted by imagination.
