Having a general group rather than specific ones would be like any other normal society. There'd still be segregation and separation simply because there are differences. That's why there's focused support groups; it ensures that the people are able to address the problems specific to them.
When it comes to things like your preferred sexual orientation, it's hardly a breeze for the self to accept it and/or to tell those closest to you. If you place them in a group where everyone is different, like in normal life, they are only going to keep to themselves still due to the pressure, other people's opinions and hatred; you just end up with the same situation and make no progress.
Like NAM says, humans are like that. They fear things they don't understand, and putting a person in the same situation they are already in but with a different background isn't going to change things.