There's also the fact that's he's not just wearing Kevlar but what looks to be heavy reinforced armor. It doesn't mean he's completely bullet proof but I think it works.
I don't think anyone's arguing that steel can be thick enough to not let a bullet penetrate. Moreso just that it wouldn't matter, he's still gonna have every rib broken and be internally bleeding so bad he's pretty much jello. Impact & shock is enough, same reason it doesn't matter how awesome the stuff Iron Man's suit is made out of is, he gets hit with some tank shell and he's spaghetti in that thing.
Armor, plate or otherwise, is fair enough for a shot of two from a handgun, obviously far better having it than not. But yeah, "sprayed on full-auto by two guys from three feet away using fancy high-end submachine guns" is a little much, if we're trying to justify this at all rationally.
Which is why we shouldn't try, and just go with it.
Does seem kinda funny with superheroes wearing their hair longer though, how they stuff it all in some form-fitting cowl. Not like Batman's exactly gonna care how his hair looks upon taking it off after a night out breaking teeth, but still.

