I have played EVE for several years now. Although there are no big LGBT corps that I know of either. Many of the big name places are accepting and openly protective of things like Orientation etc.
EVE University the teaching Corp is a perfect example. To be a member of it you have to be respectful towards others. Do not scam, cheat or steal from others.
Although many groups seem to have the Xbox Live CoD mentality at times, EVE Uni rejects that.
"EVE is a game about being the biggest bastard in a universe of bastards, and we are running a charity?"
Other groups will hold similar mentalities and not stand for abuse of their members based on anything like that.
CVA is a Null Sec alliance of Corporations that someone keeps suggesting to me as a good group. I have yet to decide though as I have been on EVE fairly briefly since joining STO.
Most will have their own forums etcc like here and you can do some digging to find those that operate more friendly inter-corp actions etc.
You will see a lot of hassle in the "Local" channels as those are unmoderated and usually used to Bait or Grief people into stupid actions.
CCPs own channels such as Rookie Help etc are moderated and will not allow grief or abuse as well.
EVE has that odd kind of social experiment to it where they leave you to do most anything and moderate each other.
As to threats of constant war decs etc. A lot of the time people like that will be all talk. Others may try it just to be viscious and grief others. Aka the Goonswarm mentality.
If fairly new to EVE and you are looking for a big group that will accept and defend you from abuse about sexuality etc then you could do worse then EVE University. Just be aware that they do have strict rules when it comes to stuff such as Wartime SOP etc.
