Assuming you're asking in good faith from curiosity...

“Neckbeard”. Hair naturally grows on the neck. So we are okay with beards, but if you don’t shave the neck, you’re judged negatively?

The "neck beard" as a facial hair style is associated with hair only on the neck, not as part of a full beard. It's often associated with a cluelessness about personal hygiene or style, because it's not something that actually looks good on anyone. Because of this, it's usually a product of ignorance, neglect or depression. The stereotype includes a certain lack of awareness of personal grooming.

“Incel”. I think this means “involuntary celibate”, right?

Correct

Why in the world would you judge someone based off this?

Normally you wouldn't, in fact the originator of the term intended it to be neutral and without judgement, however the term has morphed. It's been adopted by a subset of extremely toxic individuals online, who blame others (society, more successful men, but especially women) for their romantic inexperience. The spaces they inhabit online are full of a nearly cult-like mentality, and the worst of them support such abhorrent ideas as human trafficking, sexual slavery and rape as natural and justified.

I don’t understand how liberals have these weird derogatory categories to put people in.

No idea where you got the impression this was a "liberal" thing. That seems like a very strange assumption to make. It's a very widely known internet subculture/stereotype that's been around for at least 20 years and has been generally apolitical. The only line you could draw between the stereotype and politics would be perhaps the rampant misogyny, in which case if that makes you immediately think only liberals could be against that maybe you should do some self reflection about the "side" you're on.