When women (the Polgar sisters) have performed well in open chess tournaments, they have been discriminated against and pressured to go play in women’s tournaments instead. They’ve been denied grandmaster titles when meeting the criteria to earn them. There has been sexism in the chess world, not a welcoming attitude towards any woman capable of competing with the top men. (Of course reactions vary. Some people have been more welcoming than others.)
Also I used to watch Jennifer Shahade as part of the commentary team for chess tournaments. I’ll tell you two things about that:
Shahade normally commentated on a team with two men. Just as with other types of TV teams, different people have different roles. She was assigned the role of having charisma, being more beginner friendly, asking questions, and showing off less chess knowledge, while the men had more expert type roles. Then one day, one of the men was busy for 20 minutes or something and temporarily left the broadcast. Without missing a beat, Shahade immediately switched to doing his expert role while he was gone. Then she switched back to her usual role when he returned. She was capable of doing the expert role the whole time, and was more multi-talented and better at role switching than either of the men.
Years earlier, Shahade was sexually harassed by one of the men involved in the chess broadcasts. This came out after he started sexually harassing another woman, which Shahade took offense to, so she complained. The result has been that neither of them (Shahade or the man) has been on the broadcast team again. This happened a few years ago in the U.S.