I remember an episode of Law &amp; Order: Criminal Intent that I translated, where the bad guys paid homeless people to look for any kind of personal documents in the garbage, precisely for the purpose to steal identities. It was quite an operation. I don't know if such a thing is an actual possibilty here. But if you've ever thrown out a piece of clothing, there's a good chance someone is wearing it right now.
If you are concerned, you can minimize the risk by throwing out your garbage late at night, as the garbage truck will pick it up soon. Also itt's unlikely someone will go through the trash at night, especially if the dumpster isn't near a streetlight or something - it's dark and they don't exactly have torches. Sometimes people do this with bags of clothes too. They know that if they throw it away in daytime, alf an hour later the area around the dumpster would be littered with their grandfathers shirts or whatever the garbage diggers didn't like. It's not a pretty sight.
But if you want to "donate" something, leaving it by the dumpster is a good option.