Frankly with that kind of a bore I'd be smiling sweetly and finding that I had something very very urgent to do somewhere else away from him. I'll take the Reeves approach: 2+2 make 5? Certainly. Enjoy. Bye bye now. But if you want to...
I'd start with why he thinks women's single sex facilities exist in the first place? Does he feel that those should be ended because treating men as potential threats are wrong? Or is there something in there about privacy and dignity? How does he feel about women's entitlement to that?
Should that entitlement be overriden by a man's desire to be present with a woman as she undresses, requires a strip search, post rape exam, etc? What is it about him Y chromosome, dick, obvs that makes him a more important kind of human being than her? Is it some biological born duty to women to sacrifice themselves for others? Let the misogyny roll.
What shall we do with the women who cannot use mixed sex spaces? If he digs out the revolting racist/xenophobic/religious intolerant stuff at this point that such women just need to stop all that nonsense and be like him, I'd frankly let him rant and get it all out in front of everyone (but you have him if he then tries the 'ner ner, women who want rights and privacy are extremist right wing' silliness)
It's not about men being a threat, it's about men with gender identities being no different in any other way to other men, and women having an entitlement to not have to subordinate themselves to a man's personal belief system (which, unfortunately, proven by law many times is sometimes 'this is a really cool way to enjoy a sexual thrill/access victims').
I don't care if a man is Jack the Ripper or has just been awarded sainthood. I don't care if it's his deep and sincere belief or his fetish. It's not my problem. I want and need sex based spaces, services and resources, because that is my access need and my life does not revolve around what may or may not be happening between a man's ears or what efforts he's gone to with medication or surgery. I absolutely want him to have accessible provision and whatever else he needs alongside, I want answers that work for everybody. But I will not be setting myself or other women on fire to keep him warm.
Smug bloke can smug off. And let's face it you could go straight to the jugular here and stop all the messing around: just inquire why he is so enjoying the thought of distressed, non consenting women being forced to submit to men in their spaces. Is that something he finds exciting?