If you are paired against an opponent and choose not to play against them then you get an uncontested match loss and will tank your ELO pretty quickly. This is also anecdotal but I've never met a player who would refuse an opponent of roughly equal ELO

That specific scenario wouldn't make the tournament a "men's only" tournament, it'd just mean that a bunch of sensitive weirdos are throwing a strop because a woman is in the vicinity lol

That's so mad though, are there really men who refuse to play chess with women???