Personally, I don't think it's appropriate to put your feet, w/ or w/out shoes on the seat.
I mean, if it is not proper etiquette to put your elbows on the table, how can it be proper to put your feet up on the seat where someone else is going to be sitting?
And you say "my feet are clean, my shoes aren't". Your feet have been in those dirty shoes. So if it is a closed in shoe - then its a stinky feet problem,and if it is a sandal type thing, then we are talking dirt and dust.
We wash our hands before meals (hopefully), if we start going barefoot in restaurants, then we'll need to wach our feet, too.