Can HOA's ban pit bulls or other dog breeds?

If it's in the Declarations, then they can. The Declarations are a contract you entered into, probably unknowingly, and you agreed to waive certain rights. You have agreed to not own a pit bull by purchasing property subject to that document.

Take you declaration to a HOA lawyer to read and see what it actually says. He then can tell you what lawfully can be done.

A government ban is very different than a private entity enacting a ban. Whenever you purchase a property subject to a HOA, you should carefully read the fine points as to what is/is not allowed and who is authorized to amend the bylaws in the future.