Garbage strikes are annoying. Striking city workers raise hackles. But there's one sure-fire way to make all of this worse: by illegally dumping garbage all over the city. What, is the veneer of civilization so thin that the moment our precious amenities are removed, we begin to fling our trash gleefully into the street? It's probably worth remembering that for the vast majority of human history, people have done without curbside garbage removal, enclosed sewers or even a proper understanding of the germ theory of disease. These folks managed to come up with a bunch of keen things like, you know, the Renaissance, science, and industy. So I think we can probably deal with a garbage strike without devolving into shrieking, trash-covered chimps.
There are probably a few folks out there that think illegal dumping is some sort of political statement, a way to say "screw you for screwing up my municipal services." Trouble is, the only people you screw over by dumping your trash are your fellow citizens. They're in the same boat you are, so why are you making their Garbage Strike even more inconvenient and disgusting?
Grow up. Hang on to your trash as long as you can, then drive it to a transfer station. It ain't convenient, but it's a nice way to demonstrate that supposed evolutionary superiority we're always on about.