The question title says it all. In what sorts of cases, if any, could an item be muktzeh to one adult Jew but not to another?
If you designate something for your own use before Shabbos, I think it may be not-muktzeh to you, but indeed muktzeh to others, for one thing. Also, medication that is essential for you but not others might be permissible to you, but not them. The only other example I could think of--not knowing the laws of muktzeh very well--was an animal, which may not be muktzeh to its owner(s) but almost certainly is to others.
But then I started to think: would animal feed also fall into this category? What about, l'havdil, certain people (someone else's baby? Others?)? I imagine there are probably other, less absurd examples, too. Are there? What are they?