Masculinity is mostly just acting in a traditionally male fashion.
You can have a dude who is muscular, hunts, rides motorcycles, and can kick ass at nearly any sport he plays, but if he speaks with a lisp and has effeminate affectations, people are going to see him as far less masculine than a typically-male-acting 120-pound computer nerd who can't do any of these things.
That's where Walz ran into issues. He came off as spastic and effeminate, plus had a habit of telling pointless lies. At that point, it didn't matter if they tried to frame him as a football coach or a guy who works on his car on the weekends.
When I used to look at the personal ads in the newspaper, I would see in the gay section that many dudes were requesting partners who were "straight acting". That was code for masculine, in the sense that the guy would be indiscernible to the public from a straight man.
The term soyboy is typically associated with the left because these guys often have (or deliberately take on) feminine mannerisms or styles, almost as some weird rejection of traditional masculinity. Right wing guys don't tend to do this.