"I can tolerate anything except the outgroup" talks about how people more fiercely reject a group very similar to their own, yet slightly different, more than they reject groups that are actually very different.
It leads to stupid gatekeeping like "treat the male chess players better than the female ones" and small nudges will never overcome it.
If women feel put off by chess unless they have their own tournaments, then they can have their own tournaments. It literally hurts nobody.
If you want to have a chess game against women, I'm sure you can do so. They aren't stopping you from playing them.
They're just stopping you from playing in the tournament they created because others were toxic to them in the existing ones.