For LGBTQ+ specifically, Todd from Bojack Horseman. He’s asexual, and he just kind of…is asexual. It’s a major plot line of character development as he figures himself out, but the asexuality isn’t a gimmick or hook. We care about Todd and this matters a lot to him, so we care about it too. It happens to be him exploring his (a)sexuality, but it could have been anything.
Abed Nadir in Community is one of the best examples IMO of doing diversity in tv right. He is autistic, and that fact is central not just to his character but to making the whole show work. Being autistic creates jokes, it’s never the joke itself. (He’s also not precious or off-limits. Abed IS the butt of some jokes, but not his autism.) He is arguably the audience surrogate despite (because of?) so much of his “deal” being how he doesn’t relate to people like everyone else. In general no one feels sorry for him (and when someone does they look like the asshole by the end of the episode). He has a lot of classic, stereotypical ASD traits, but they are treated like personality traits. He’s a shining example of why identity-first language feels important for a lot of people: he is a complex and fleshed-out whole person as he is. If you took away his autism he’d be flat and boring and unrelatable, a completely different character.
Abed and Todd both kind of just exist very authentically in their worlds. No one (character or writer) is asking you to feel a particular way about them, just to appreciate them for who they are like any other character. If we care about the world and the character, we’ll care about what matters to them.