Steve is a guy from '40s, but he's a fairly progressive guy, being cool with non-white people and women in positions of authority. Also, I reiterate that people were having sex outside marriage in the '40s, and Steve's attitude toward what he perceives as an affair between Peggy and Howard, and really, the scene at the bar comes across as a metaphor for sex.
Don't get me wrong, I love that the movie implies Steve is a virgin, and that he isn't any less of a man for it. I don't think he needs to get laid, as others do, I'm cool with it going either way.
I also loved skinny Steve, but a main point in the first movie is that Steve doesn't change when he becomes a super-soldier. So really, he'll always be skinny Steve.