Personally, it doesn't bother me as long as the shoes/feet are clean. I've seen people pop their muddy shoes up on a chair, leaving mud and obvious dirt streaks across it. I would hate to sit down in that chair and have that transferred to my clothes - especially work clothes that are nicer than most. While outside chairs do get dirty and dusty from wind and the like, I think dirty shoes make the problem a lot worse. And inside chairs, one would not expect to find mud or dirt on them at all, so I think it's important for whomever is putting their feet up to make sure their shoes are clean.
Aside from that, I don't mind it. I agree that it does look somewhat unprofessional, but then again, the workers are on their breaks or lunch, so I wouldn't really bother taking it to management.