I had a friend that I talked to, haven't talked to recently since we disagree politically. He told me he voted Biden because Trump didn't denounce white supremacy (I showed that he did) he then backtracked and said he didn't denounce it specifically in the debate (he did lol).

But anyways, I noticed that he's absurdly sensitive overall and not just about politics. He gets butthurt any time you criticize him but he has no problem dishing it out to others. I remember he got mad at me once because I didn't look him in the eye when I talked to him. We also worked the same job together but he quit the job because he felt the boss was too rude. At this point I am starting to wonder if it's even worth remaining friends with this guy.

Not anymore. If someone can't take dark humor and healthy disagreements, I don't want them around.

This.

GF doesn't handle dark jokes very well, especially anything political or social issue oriented. Feels bad mane.

OP it's clear you identify attributes/aspects you don't like in people you've been chillin' with (sensitive/weak/impulsive). It's up to you to weigh if the redeeming qualities, past times / memories, and general idea of how the future will look with this person in terms of a relationship with you (no homo), are worth it to you. If not, then you likely know what you want and feel, and should decisively act on it. If yes, then keep putting up with the BS, try to hold back and be more careful with them, and stay positive with them. Think about it from their perspective too, if you cut ties would it really bother them? Would you feel bad about it?