Hello neighbor, New Mexico is just next door

You are right about New Mexico being a very liberal state though most of the country is now pretty open on gender issues.
For the gay supervisor I suggest you try to find some time for a one on one conversation. I suspect he will be accepting but you may need to build a little friendship between the two of you. I have never had issues with gay people but I know there are a few out there with issues. The worst are the female feminist type and I have only encountered one on the internet.
With a really large company, a meeting is impractically. If anyone has issues with you they will take it up with their boss or HR. In either case, if you need to be involved, I am sure they will pull you into the loop. For now it's best that only the people who work close to you know what is happening and you may find a fair portion of the company will not know of your history or care to know.
Know how much of your story you are willing to tell and under what conditions. Let the others know you are easy to talk with and willing to be helpful. People will come to you with questions but you may be surprised to find many people aren't interested in knowing more and will accept you whoever you are.