I don't mind people taking my trash. In fact, I use them as a reliable source to get rid of large items without having to pay anything extra. Smaller items I think someone might find useful I'll set aside on the curb and let some dude take that old box of VHS tapes to sell for 10¢ each at the flea market. Provided they don't make a mess, more power to 'em.
But if I asked someone to stop pawing through my trash and they steadfastly refused, I'm sure I'd have an issue with it as well.
My neighborhood is particularly good at leaving treasures on the curb. Things I've collected from my nearest neighbors (the ones I can see the curb from our house)
-A green painted picnic table that we use as a garden extension to hold potted plants
-A flat screen monitor (not widescreen, but it was still an upgrade for one of our computers, and now I have two!)
-A two-foot tall bird bath in the shape of a mushroom
I'm not a dumpster diver, my mother does indeed make a business out of it when the nicer suburbs have their "spring clean up" days and she usually gets some pretty cool retro furniture out of the deal, just truckfulls of swag. People are so wasteful.