Should guests at least offer to help with dishes and clean-up?

[Gwywnnydd]

I think it is polite for guests to make the offer: "Can I help you with anything?"
AND I think guests should graciously accept whatever the response is. "No, Brunhilda, I have it under control. Canape?" OR "Yes, you could take that tray of chips and dip into the other room if you don't mind, thank you."
Joy in Virginia

Yes, exactly.

If I am a guest, I have to offer to help. My ancestors will rise from their graves in shame if I don't. It's a <myfamilyname> thing :}.

If I am a host, I'm happy to hear an offer to help, and I might take the person up on it. I might say 'No, no, I've got it under control." This is largely dependent on the formality of the event.

[Midnight Kitty]

I heard this story the other day.  I don't vouch for it being factually accurate, but you can hear the "truth" in it.

The guy telling the story grew up "in the country."  He & his brother took the bus into town when they were little.  They ate lunch in a small, local, casual restaurant.  He overheard the waitress telling the cook, "Oh, Those boys so cute.  Dey mus' be from da country.  After dey pau (finished) eat, they brought their dirty dishes back to the kitchen."