Thanks for the responses.
The point of my post about the sign on the front desk of the Mill Creek Inn in Lake Geneva Wisconsin was not to opine about whether they have the right to set some parameters around the use of their facilities. They of course have the right to set policies that maximize their profitability, reputation, mission fulfillment, or whatever else matters to them.
The point I was trying to make was not about the merits of the policy. It was about the first impression made upon a guest/customer with their sign.
The policy could have been "enforced" just as well with a sign in the room, near the tub, rather than with an "in-your-face" sign propped up on the front desk.
To borrow a line from the popular Capital One commercial: "What’s your first impression?"