I wouldn't send him to a sleepover with Disney ones, but he can wear anything he wants at home. Also, older boys usally don't wear sets. Clothing boys is a funny thing -- I have three, so I should know. There's a few years, from early adolescence to mid-teens, when wearing cartoon characters seen as babyish (Sponge Bob is probably okay, Nemo would pass but not Mickey or Pooh characters) will invite taunting. Then, by 16 or so, it's cool to wear cartoons again. Both of my older boys -- 16 and very cool and 20 and a college sophomore -- have Ninja Turtle shirts. And the 16-year-old wore his Sponge Bob pj bottoms to school for some spirit week event.
Adults, of course, can wear any cartoon character they want.