It's a people problem, but the problem is you. If you don't care about what he's having for lunch, then I'm not so sure what's so hard about ignoring his tweet. It's only going to be on your screen for a split second as you're scrolling through other stuff. Presumably anyone you follow would post more things that are worthwhile than not; otherwise, you should just find new people to follow.

One of my friends tweets quite a bit about Magic: The Gathering. I don't care about that. Somehow I get along just fine by not paying much attention to the posts I don't care about. I don't quite understand your dilemma.