They low-key wanna have it die out.

I doubt it. I've met a lot of people throughout the political spectrum who don't think Japan would be Japan without an emperor. It's something of a symbol of national identity for a lot of people. Of course the rabid far-right want this, but there are a fair amount of people in other parts of the political spectrum who also want to keep it going (though most of those would be more than happy to see an empress from what I gather).

So the question is, do femboys count?

Legally in Japan, gender/sex (I know, not the same, but the govt doesn't care) is based on the downstairs plumbing, so anyone AMAB and anyone else who has bottom surgery and change their koseki to be 'male' technically qualifies. EDIT: although I don't know that the royal family actually has a official koseki in the specific sense of the legal document that all Japanese citizens otherwise do.