I say men gave away their rights. Girlie Men who refused to stand up for their rights. If they had only stood up then we wouldn't be in this mess. And now men are reaping what was sown when they tried to pacify feminists groups. Their sons are being turned into girlie men in the public schools. Women didn't take away men's rights. Men didn't fight for their rights.
You can't have your cake and eat it, too. Before I explain, let me just say that I agree with your sentiment that "tit for tat" tactics won't really advance the conservative agenda. It might be viscerally satisfying, but strategy is called for to prevail in these situations. Fighting back in the courts through civil cases, and overturning the legislation in the federal and state legislatures, is the course of action that leads to long-term results.
That being said however, when one advocates fighting back, one shouldn't be overly sensitive when the tactics of fighting back happens to gore their ox during the fray. You can't bring suit without cause, and the courts being where these abominable laws were created, they are one arena where they must be beaten back.
Now, if you are able to offer legal advice on just how to engage in the court system without deliberately creating a test case like this, I'm all ears. We could bring suit against any number of women-only clubs like golfing or women-only business networking clubs for example, but we would only end up goring someone else's ox, and not your personal ox. Someone, somewhere, will have their personal lives touched by this, and be unhappy about it.
Note that I understand this guy might not even be provoking a test case; he might be a complete nutter for all we know. Sure, then I'm not going to back him because his tactic is not part of an overall strategy to overturn decades of unjust feminist dogma. Even if he wins, the precedent will not advance a liberty-minded position if it merely is used to bludgeon all-women clubs as well as all-men clubs into places where men nor women wish to congregate. That way lies the madness of the leftists we all recoil from in disgust.
But somewhere in the fight to shine the light of truth upon the injustices created by extremist feminists, unless there is something about our adversarial judicial system I don't understand that you could perhaps enlighten me upon, we have to start establishing precedents so we can point out the contradictions and set the foundation for overturning the laws in the legislatures. The feminists who set up these legal edifices didn't achieve their victories in one fell swoop, and neither can we expect the conservative movement to simply strike down these laws overnight. Marketing-wise, women's fitness clubs are an appropriate lawsuit target because they affect so many people, and it brings much-needed attention to the injustice. Unfortunately for your personal situation, you see that action as a threat (rightly) to the benefits you incur from attending your women's only club.
I believe the lesson we should take home from all this is that when a part of our civil order gives up its rights, we are all diminished by it and will suffer hardship trying to bring back the surrendered liberty. Tyranny thrives upon the timid who lack the courage to endure hardship to obtain liberty. Your liberty to attend single-gender clubs is secured by a farce because it is protected not by rule of law, but rule of political correctness, whose judgement is rendered by thugs and not impartial, objective standards. Challenging cherished female-only institutions protected by this political correctness is a valid tactic to point out the defective laws applied unequally to men-only clubs, and applied in that manner only due to political correctness. That sets up the legal and legislative crisis we need to force a decision: strike down the laws, or admit due to political correctness there is unequal protection under the law.
In other words, the day extemist feminists won court rulings in their favor, is the day we were going to have to break a few eggs to smell the omelette of liberty again.