The feeling you're experiencing has a name: it's called "cringe". I can't watch Frasier for more than about half an episode because of it. Or I Love Lucy... same problem. But Seinfeld, which has plenty of the same humour mechanic, always seems to manage to stay just below the threshold for me.
Halt and Catch Fire is really, really good. Please trust us. Give it another shot. Skip forward a bit when you feel the need to. Skip the first episode entirely and just read a synopsis if you need to.
A related thing I find difficult to watch is when characters are in impending danger too often. Breaking Bad, for instance, was a bit hard for me to get into because of the continual tension and risk of everything going sideways. I managed to watch it anyway and am glad of it, but definitely found Better Call Saul to be a more pleasurable watch.