OP, I am 51 yrs old, so I don't think age has much to do with conservative POV. It's based on the individual, not a number. Just wanted to get that out of the way.
Also, you may want to break up your OP so it doesn't read like a wall of text.
You certainly have the right to your opinion, but so does your girlfriend. You are walking into a situation that has existed for years. Asking her to change all of this is a bit much. The issue really is, can you live with things the way are? If you can't, then this is not for you.
I do believe that men and women can be friends. I've always had a good number of male friends. And, yes, they've only been friends. I have zero interest in anything more. I don't do anything with said friends that seems hinky, but an occasional dinner, movie, or concert - no problem.