As a gay male, I often have an additional wrinkle - in the Masonic orders, Eagles, Elks, or Moose Lodge, I feel I would be the odd man out in these situation.
I was in the Masons for a number of years and I was surprised to read your post. I'm quite sure that some of the Masons were gay. It didn't matter any. The only time that I could see someone feeling like the odd man out is where there are events for couples and you didn't feel comfortable bringing a guest. This would be more true for the Shriners than say the Blue Lodge (plain Masonic lodge).
I recently became an Odd Fellow and I still feel the same with respect to whether a member is gay or not. The big difference with the Odd Fellows is that both men and women can be (and are) members. The Masonic orders are only for men.
In any case, I wouldn't write them off completely due to your concern.
To clarify, I also know a few gay men in lodges, sexuality isn't an issue there.
Being recognized as a good guy by a bunch of other guys is no small feat. Someone who is trustworthy, kind, fair minded, honest, with only moderate conceits, good natured, charitable, and magnanimous is rare to begin with. I think if someone has these qualities, there is very, very little that will stand in their way.
