I'm honestly pretty baffled why the default response to anyone being against this idea on a philosophical level is to assume the absolute worst, that person is an MRA woman-hating hypocrite who only cares about equality when it directly effects them. That's a pretty big assumption to make, I'd say.
The real-world repercussions of this single movie theater excluding men on a single weekday in a random town are negligible. Especially with the press it's getting. There will maybe be 20 - 30 dudes who go that day, unaware of the stipulation, and will be turned away. Not a big deal.
But from a theoretical standpoint, I can't say I support the concept. Of course women have historically been marginalized, and that's an awful thing. But the goal of a free and just society should be equality for all humans, where elements of their existence beyond their control (race, sex, orientation, etc.) are complete non-factors in how they're able to operate and participate in society. I don't think excluding someone from a public good or service based on their chromosomes is a wise way to progress closer to a nondiscriminatory society, the same way I wouldn't be okay with this concept if the script was flipped (the next Superman movie having a boys-only screening for a day, for example). I've also always found it odd that it's legal to discriminate based on sex at certain clubs or bars - women get in free, men have to pay. Obviously I understand why it makes sense from a business and marketing perspective, but I've certainly never understood the underlying ethics as to why it's legal.
Again, I hope I'm being clear enough by stating the real-world consequences of this lone theater hosting this event are too negligible to matter in any meaningful way. But I still think it's an interesting jumping-off point for discussions like these, because in terms of what an ideal society should be, public businesses that can refuse service based on something found at the DNA-level wouldn't have a place in it.
*takes deep breath, prepares for an avalanche of vitriol*