Honestly, i think it depends on a number of factors.
Authoritarians are loyal to their in-group ideology first and foremost, but most of them don’t really want to be a leader: theyre usually too scared they’ll do something that loses them the affirmation they need. They prefer to follow someone else who will confidently take control & set boundaries for them instead. So they’re not really seeking validation from existing leaders (though if an existing leader validates them, they will be loyal to them): it’s more like they’re constantly on the lookout for people who already validate them but also are willing to lead them.
As a result, anyone who says ‘I agree with you and I will tell you what to do’ tends to become an authority in the eyes of authoritarians. They will raise the wannabe leader up from obscurity themselves if they have to.
And I do mean anyone. You might have more of an uphill battle if you don’t fit their mental image of a good person – for example, a 30+-yo fandom anti might have a harder time gaining trust than a minor or a person in their early 20’s – but if you say the right things, make them feel good about themselves & their choices, and keep them busy with enemies to fear and attack, you’re likely to find favor eventually. (Or you could just lie about your age until you’re popular enough. Once you’re an established leader in an authoritarian group, it’s hard to do wrong in their eyes.)
So all that said:
militant fandom antis are still fans first and foremost. So like many people, they seem to first seek validation from the show creators and staff. If the staff validates their opinions, condemns ‘bad’ ships & shippers, etc, they will stan those staff members. They will also feel they have the blessing of the staff to police the fandom however they like.
However, if the staff do not validate militant fandom antis, they will reject the staff’s leadership as deficient, cowardly, and/or deviant/dangerous. They will try to ‘remove’ them from what they see as undeserved positions of authority by undermining their character, threatening them when they say things antis disapprove of, and trying to silence them. (If targeted creators resign from staff, delete social media, or publicly apologize/bow out of defending non-antis, that counts as success.)
Either way, militant fandom antis also raise up BNFs from their own social circles – people who say the right things and attack the right people, and are willing&eager to act as an authority, creating arguments for other fandom antis to parrot & setting boundaries around good and bad behavior.
(It’s not a coincidence that these leaders tend to be the meanest & angriest militant antis of all.)
Antis are fucking terrifying