There's also the massive general exemption of wether or not your actions are discriminatory.

For example, it's perfectly legitimate to reject an actor who's gender doesn't match the character they are being hired to perform. That is not discriminatory. It's only discrimination if there's no valid reason to reject someone based on gender.

The court ruled, in this case, that there was no valid reason to prevent men from viewing picaso/etc's artwork. "We want to make a point" is not good enough.

I’m not a lawyer, but from what I’ve read, I think if they were to do the paperwork to set up the room as a women-only club somehow, they’d be in the clear.

I'm not a lawyer either, but I don't think the law works like that. Nuance matters in legal proceedings, and finding a loophole like that might reduce your damages but it won't prevent you from losing the case. When two pieces of legislation disagree (e.g. no discrimination vs allowing women-only clubs), it's basically up to the judge to decide which one has priority and they're likely to choose the one that's most important. Which would be the anti-discrimination law, not the club law. The world is full of contradicting laws - judges deal with this stuff every day all day and cases where the law is clear generally don't go to court at all.

Fernwood, a women only gym, is allowed to exist.

Because there are sections of the law which allow exemption from the gender discrimination section for various reasons, and they have successfully argued that there are benefits to having a women only gym which are important enough to deserve an exemption (to provide substantive equality). They also only allow women patrons, so men are not charged for a service that is not equally provided.

I don’t really see it as problematic for a discriminated class to seek to foster a space free from those who perpetuate that discrimination

Neither do many other people, which is why such examples as Fernwood have received exemptions from the law and why there is a specific exemption in the laws for both female and male only clubs.

I don’t think it sets a precedent for protected classes to be discriminated against as “art” because men aren’t a class that needs protecting

Allowing discrimination based on gender without substantiating the businesses eligibility for an exemption under the law absolutely would set a precedent for the courts. While you may agree with this particular case of discrimination it is not a good idea to open an opportunity for more discrimination in the future - keep in mind it may not always be the type you agree with.

I wonder if they think it would be ok for the women to be in the men's bathrooms at the same museum? Sure there are separatel women's bathrooms, but do the women's bathrooms have urinals for them to use if they wanted to?

I don't think there should be a women only space in a general museum, except to make a point, but the cost of admission is not the argument to win that fight. If it's to make a point, it shouldn't be enforced.