My dog sheds in the common area, but I'm not going to clean it up.
Why wouldn't you clean up after your dog?
I think dog hair is not that harmful and if it bothers my neighbors that's their problem.
It sounds like your dog leaves a lot of hair in the common areas. If you're going to have a pet you are responsible for cleaning up after it. You might get kicked out of your housing if you don't.
No one gave me a warning letter so I'm not worried.
Just because you haven't received a warning letter yet doesn't mean you won't in the future. Wouldn't you feel irritated is someone else dirtied the common area? Cleaning up after your dog is the neighborly thing to do.