They're conservative in my area. I'm in a red part of a blue state. Maybe it's different in NYC?

They tend to lean that way, but the VFW , LEGION and DAV primarily support veterans.
I also think that the Moose and Elks are good organizations.. I just really don't talk politics and get along fine. Like everything, there are good and bad things ???

I live in what some would consider a mixed area but I find it to be conservative. Even groups that are secular tend to end up with a lot of religious people and discussion, and the default setting is for them to assume I am as well. The only variance to this is the Asian organizations. I've found that even when the people belong to religions, they tend to consider it more of a community/networking thing. But I have recently, here and there, found more and more freethinkers, so if you can ignore the others, it may be worth pursuing the ones you have an interest in, and maybe you'll get lucky.

Freemasons are forbidden, by their charter rules, to discuss religion or politics in the Lodge. If I were ever to join a fraternal organization, it's Masons for me. (Plus, maybe they really do rule the world, in which case I could get in on the action.)

I don't know, because the only time I've been to one of these places (Moose) is to attend a wedding reception or retirement party. I know they have that type of reputation in my area, though.