So I was watching old House MD reruns and while there are no doctors or any recurring LGBT characters so far the place is full of queer representation.

There's the Lesbian couple who have a baby treated by Dr. House(The baby dies it's very sad) and they were shown to be an extremely good couple and parents to this baby

There's the senator running to be the first gay president and first black president. (The season was before Obama was elected) 

There was the gay man who decided to give up on morality after he got HIV. He got kicked out of his house because he got HIV and therefore couldn't be a donor to his mother when she was dying. The family gets a huge story arc which takes most of the episode. They also show that getting HIV isn't a blame thing by having one of the doctors get coughed blood on by the infected person and having her insist the whole time that it wasn't his fault.

There are many more including gay parents, LGBT teens, people of all races, people with physical and mental disabilities, people of all body types and probably much more but I'm only halfway through season two. The one thing I haven't seen is a trans or non-binary person. But again I'm only halfway through season 2 and there are so far 8 seasons(I'm not sure if it's been canceled yet I'll google it later)

It's a pretty progressive show and often shows that we judge people too harshly and make assumptions we shouldn't.

For instance, everyone treats House like a broken little angel because of his disability. But because of that assumption, he gets away with being an asshole to a lot of people who treat him special.

Or one of the girls in an episode who suffers from obesity and one of the doctors is very judgemental but as it turns out she had a condition and that wouldn't let her control her weight and her efforts to do so while doctors refused to help her is what made her sick.

I can't think of any others off the top of my head but it's a pretty awesome show