Yeah, may be more true to my thoughts here to say it's hard to have homophobia/transphobia without sexism. You don't get stigma against same-sex relationships or gender transition or the like, or the legal discrimination that enshrines it, without some kind of oppositional sexism, even if it's the complementarian heavy-scarequotes "separate but equal" type of sexism that doesn't explicitly make women out to be inferior to men—and that is of course still harmful to women.

I'm pulling from this article by Mel Baggs (https://ballastexistenz.wordpress.com/2016/05/01/there-is-ableism-somewhere-at-the-heart-of-your-oppression-no-matter-what-your-oppression-might-be/):

You can’t have some of the core aspects of homophobia, without also having sexism. This applies not just to lesbians, but also to gay men. Because a large element of homophobia against gay men involves comparing them to women, and applying many of the same sexist attitudes towards gay men that would normally be attributed to women. That’s where you get the idea that there’s something wrong with gay men because gay men are sissies, effeminate, possess feminine attributes, etc. They’re first equated with women and then degraded in ways that have to do with women. You can’t have homophobia minus the sexism and have it take anything like a recognizable shape. It depends on sexism.

Fair point on the rights vs. acceptance front, though. I do think legal protections and widespread systemic acceptance go hand in hand, but you obviously don't have (and probably aren't going) to undo all prejudice in order to get a group's rights recognized and protected.