Regarding sexism; most tournaments in Chess (including the world championship) are fully open and are thus gender netral: anyone can participate regardless of sex/gender and will compete on equal footing.

Women only categories have been created to give women visibility because they mostly were not able to reach advanced levels in the open format.

Some women choose to compete with men (Judit Polgár being a somewhat recent example) but most go straight to the women only tournaments to have a shot.

The men vs women « bias » is not unproven, they litterally had to create entire categories of competiton to account for it.