I bet it wouldn’t. We have a collective image from films. People back in the day had no such imagery. Cowboys were poorly paid agricultural workers.

Coming into a saloon kicking in the swinging doors (if they had them) would have only startled and pissed off the guests, and the owner would give you the stink eye and covertly spit in your drink if not just kick you out. Doors are neither bombproof, nor free.