You can have a no dogs rule. You just can't have a "No service dogs" rule. Service dogs are essential to the welfare of their humans, denying them would be like

You can have a no dogs rule. You just can't have a "No service dogs" rule. Service dogs are essential to the welfare of their humans, denying them would be like having a "no glasses" or "no canes" or "no pacemakers" rule disallowing folks who need assistance. Yes, there are limits, especially if the area is dangerous or the dog is disruptive, but generally that dog should be considered to be a tool the human is using.