I can easily listen to podcasts while doing household chores. Most podcasts aren't that information-dense anyways and while retention isn't perfect, you get an overview of a topic and can still dig deeper (or not) later. Or to flip it around: most podcasts don't give you that much benefit anyways.

I think the answer is actually the other way around: It's the chores that don't require much attention.

YMMV but I sometimes listen to a podcast or audiobook while playing mindless video games. I can't watch a show while playing video games, since I need to actually watch the screen. Since the game doesn't require mental thought, I can still pay attention to the content of the podcast.

+1 to this.

Personally, I listen to podcasts while biking or driving; I can't just sit and listen to them, I need to be physically doing something.