Can’t speak for the hillbillies but Lucy stands up, for the most part. She was a real one. It is funny seeing hers and Ricky’s separated twin beds for filming, though.

The Bevery Hillbillies is still pretty side-splittingly funny. Standard product-of-its-time disclaimer applies.

Edit: Honestly, watching their asshole bank manager neighbor get shit on in every which way is all the funnier, today.

I haven't watched The Beverly Hillbillies lately, but the nursing home I worked at had DVDs of I Love Lucy. It still holds up, in my opinion.

As to classic, old shows that feel out of place today, I'd have to go with Looney Tunes and similar early cartoons. Even watching them as a kid, the violence and sexism felt really weird to me. A lot of the "humor" came from physical violence or cross-dressing honey pots, which felt tired, repetitive, and not funny to child-me.

Then a lot of those old shows had stories that involved two male characters fighting over a female character. I remember thinking, "What is this? If two guys started a fist fight over me, I wouldn't swoon over the winner, I'd walk away from both of them for being violent at the drop of a hat."