I rather like western lesbian romance novels (Georgia Beers and Karin Kallmaker are particularly good authors) and for the most part they don't include a whole lot of anti-gay environments.
Do they have friends who support them (or simply don't care about their orientation and accept them for who they are)?
As a general rule, yes. Most of the lesbian romance novels I've read, although keep in mind I generally stick to award-winners like Beers and Kallmaker so there's a certain level of quality, the main characters are generally surrounded by supportive friends, co-workers and family. And the women in question (with the exception of one story that was about a woman belatedly discovering she liked girls) are pretty much all out as well. It's a nice world to visit, for sure.
Bit of a sidenote, a thought: A lot of japanese mangas make me wonder if they even have friends, do they hang out with a group of buddies and just chill?... The general anti-gay environment is usually reflected onto the characters' thoughts "but we are both girls." or keeping things secret from faceless and nameless background characters, rarely see groups of friends representing a closer environment to the MCs.
Agree with you on that, can't really think of many like this one where you've got a little mini-community that accepts its members' ways without question. Although stuff like Beck, which I mentioned before, does give a peek into underground youth culture in Japan which largely doesn't make it into the mangas.
I wish it would, it's fascinating stuff. I'd love to see a yuri manga that gets into the Japanese punk scene, for instance.