To me this whole thing kind of looks like baiting - young men have had it worse than women for quite a long time now, but then they are offered a shortcut for succeeding on the easy setting. Just become a woman! Sort of...

But that has to be rather tempting for some percentage of frustrated boys and young men. Especially those ones who would want some sort of easier shortcut to success and fame instead of having to work hard.

And BTW, also bullies, presumably, as the members of any currently "protected class" can do that while always being able to fall back on the pretense of being something like a persecuted minority you should not touch if you are decent person if anybody tried to make them responsible for their actions or to punish them for those.

And of course once you have weakened the male part of the population in any country it becomes easier for any group that still has more aggressive men to take over. They don't need to get everybody, but the larger the percentage of the males the better for the invaders. Women also, in deep down at least even when they are not willing to acknowledge it out loud (read any really successful romance stories, Twilight and 50 Shades of Grey come to mind - what are those "dreamy" male characters like, and how do they treat the POV female character?), usually prefer the more masculine types who would be able to protect them even in more hostile environments, so at least a percentage of them would then be more interested in those men from the more patriarchal society. Which will of course also help any type of invasion, in whatever form the invasion happens.