This is a great resource to the LGBT community of FFXIV. I know I was in an FC in my early days that was pretty homophobic (got out of there right quick!)—I think it's great to compile a list like this so others don't go through similar experiences. =)
That being said, I'd like to plug my current FC. I believe we'd fall in the LGBT-Friendly category.
The Unbroken — Diabolos
unbroken.guildwork.com
"The Unbroken is an all-inclusive (meaning multi-racial, multi-religious, and LGBT-friendly) casual Free Company on the Diabolos server of Final Fantasy 14: A Realm Reborn accepting anyone who is mature, friendly, and respectful."
(That blurb is taken directly from our website, on the About page)