The community doesn't exist solely to shelter people from, and campaign against, homophobia even though that is an important part. It's also about meeting other people with shared experiences, and finding support and companionship with people who see the world like you do. I am asexual, I am romantically attracted to women, I'm not homosexual and so my experiences would be different from those of a lesbian.
But banding together against discrimination is a big part of it, loopsdefruit. I don't have a lot in common with many gay men apart from I haven't been able to walk down the street holding hands with some of my partners.
And as for finding things in common - the thing you have in common with lesbians, even if you don't identify as a lesbian, is a romantic attraction to other women. That's your entry point into the LGB community. You not having sex is not the thing you have in common. If you want to band together with other women romantically attracted to women who don't have sex, then knock yourself out, it still comes under the LGB umbrella. But if you want a community group of women who just don't have sex, and some of those women aren't romantically interested in other women, ever, then that's not an LGB group at all. That's just a group of asexuals, which is fine.
As for bisexuals: I am bi whatever the sex of the person I am involved with. But if I am involved with a man, it is not a queer relationship, even if he is bi or queer or whatever too. It's a straight relationship, and while I would feel entirely content still taking part in community life, etc, I would still have to acknowledge that in this relationship I was benefiting from straight privilege. I would also consider it a bit of a dick move if I went on marches, etc, with a male partner and was all PDA all over them, as that's just not the place for flaunting straight privilege. (I don't think I'd go with a male partner to a pride march, even if he was bi too. I think I'd go with my women friends and let him go with his friends. Although it's never come up in real life.) Most bisexuals are in relationships with people of the opposite sex, btw.