Sex and gender minorities doesn't include lesbians, gays, and bisexuals. It would be a term that excludes LGB people. Let me say it a third time: you want to exclude LGB people from the community that they created, which they form the backbone of.

Why? Lesbians, gays, and bisexuals are not necessarily sex minorities: most don't have differences of sexual development, so there are no complications in their sex identity. Most also are cis, so they are not gender minorities. Sex and gender minorities sounds like a term for people with DSDs, trans people, non-binary people, and other people with different genders. Your term explicitly excludes sexuality, which is the sole defining feature of LGB people as LGB people.

And just to drive it home: your term excludes lesbians, gays, and bisexuals from their own community and political movement. I'm not sure how you could be more homophobic without just going full hate speech.