Anti-sexism might still be sexism, but with a non-negative connotation.
The question is ill-defined, those terms, sexism and natural ..., don't have to be mutually exclusive. Thew comparison doesn't even make much sense, see also https://en.wikipedia.org/wiki/Appeal_to_nature
Your implication is paradox, because it paints with a pretty broad brush and out of line. You suggest that discriminating against naturally gender specific behavior is sexism. I don't think that's the case, although it's a loosely defined, broad term. At least sexism is a stereotype, too, yes.
Paradoxically, women who are discriminating against men would be assertive. Therefore you would be in turn discriminating against this presumably unnatural tendency (unless women aren't vocal about this). That's ironic because as far as I know sexism fundamentally is against ascribing any character attributes based on gender, analog to racism. (I might be confused here, because it's not usually my debate. Popular sexism is rather against discrimination in face of obvious gender based properties, like pregnancy.)
On the other hand, casual sexism is just the exercise of sexism, whether it be natural or not, in settings where it doesn't belong. In general, professionalism requires an extend of discretion and privacy and is certainly not black and white at that, but rather subjective. And that's what emancipation is about, incidentally, to be treated as a subject, individually, and not objective as a stereotype.