Labels as such are rarely okay IMO, though I've mostly seen the latter of those two come out as a common joke between spouses -- I've seen it used both ways, actually, though it's usually more frowned upon when labelling a man ("What? You're saying he's automatically better than you because he's a man?"), which wouldn't be such a loaded thing to do if it hadn't been for the long struggle for women to get out of being 'property'. (And no, it's been a long time since they were seen as such, but it'll probably take a couple of more decades or centuries before people stop with the knee-jerk reactions.)
I... wouldn't count it as radical feminism, to be honest. It's not the whole picture, but it is part of the package. I know of trans men who've been accused of merely wanting a higher paycheck, or of being feminists (strange as it may seem). They also tend to pass under the radar when it comes to being taken seriously by medical staff (male behaviour and clothing being a lot more acceptable for biological females than female behaviour and clothing is for biological males).
Which is also pretty much why people are arguing for unisex outfits, even the more feminine-looking ones. And yes, we are approaching gender equality. "Letting" women wear men's clothes (e.g. pants) is one part of it. Letting men wear women's clothes (without being beaten and/or mocked) is one step we haven't gotten to.
Personally, being on the male side of the fence, I see it as fairly obvious that one of the larger underlying reasons to the reluctance to such behaviour (men in skirts) is the unwillingness to appear weak, feminine traits being seen as weakness in a man. It's slowly getting better, of course, but when I grew up boys were still being taught not to cry, not to show emotions, because only girls or babies do that. Boys liking pink immediately being mocked for it by other children, because it's a girl colour. (The italicized words often said in a mocking tone.)
I'm not talking about swearing and spitting, though. I'm talking about "masculine" qualities such as strength, leadership, self-confidence, courage. And no, I don't think those should be considered male traits at all, but a lot of people do. Just google 'male personality traits' ^_~
(Though as a note, women exibiting the same degree as a man of certain behaviour patterns tend to be described in very different terms than the man would. So I'm well aware that it's not as simple as that.)