I'm a man, I'm not cis because cis is a load of bollocks.
I'm very invested in the discussion because I have a wife and daughter and I'm on Mumsnet, which has opened my eyes to what's going on.
I don't think most men are that invested in the discussion though. Unless if has affected the women in their lives in a meaningful way, they don't see how it really affects them.
The only thing that's really registered with them is that you can get cancelled for wrong think. Maybe they're Father Ted fans who've heard what's happened to Graham Lineham, maybe they've read a couple of Guardian articles about the evils of JK Rowling. So they parrot TWAW, and consent to putting pronouns in their emails, and generally just don't engage with the subject.
The vast majority of men haven't really registered the news about the supreme court, haven't noticed the winds are changing. They don't know that you don't get cancelled any more for saying TWAM, so there's going to be a certain amount of inertia there before they finally notice something has changed.
Of course there are exceptions. The Owen Jones' of this world, who are so lefty that they can't possibly conceive of not being on the side of the "most marginalised" group, or the ones who see this as another way to control women.
But most men, just don't know enough about the topic to care, to think through the consequences. And some of these men are politicians, CEOs, in charge of the media. They don't want to have to think about this, so they farm it out to Stonewall to handle for them.
Things are slowly changing, and they're starting to wake up. I've had a few conversations over the last few months that started with "Vimes, you know about all this trans crap, what's actually going on?". But mostly that inertia still rumbles on.