Well, your approach requires the collection of identities associated with particular political alignment(s). And that you need both pieces linked together for it to work - where neither alignment nor identity mean anything separately.
Aside from public figures, that is very much in the realm of doxxing.
You don't need to gather any identifies to document simply quite a stupid group that will gladly scream out to the world of their own accord how stupid it is. Magas don't even need any one else, they are quite happy to screech mindlessly anywhere and everywhere.
And you still didn't say how you will "prevent" others from embarassing the administration and it's voters without violating 1A or even why you feel so triggered at criticisms of these idiots that you get so passionate to the point of violating the constitution to prevent them being shown for their stupidities.
What exactly do you think "my approach" is btw lmfao?
edit: Weren't you whining just a few days ago of bluesky being too cloistered, first I don't understand how a website that anyone is free to join with even less details than twitter is more cloistered, and more importantly why is cloistering and shielding a group from criticism suddenly good when its magas? It's pretty hilarious I have to say.
Aside from public figures, that is very much in the realm of doxxing.