not bar women from public spaces.

This isn't barring women from public places, it's a private establishment for men only. I think people are mainly upset about it because of how they pitched it.

If they just pitched it as a men only gym without any other reason, this probably wouldn't be post worthy.

There are plenty of women only gyms within a 30 minute drive of where I used to live (a more metro area). Nothing to care about.