Their house, their rules....
In general, I tend to agree with this sentiment and I'm fully OK with voluntarily playing by the house rules. So long as it is voluntary.
The implied "But" is this case stems from the use of law to enforce what would be in any other case 'Discrimination'.
SAF, Comm2A and others are correctly pursuing 2A as a Civil Rights Issue. If keeping and bearing arms under 2A is truly a Right (and it is...) then private, commercial businesses cannot discriminate based on exercise of that Right. Discrimination based on race by private businesses is clearly not legal. Like with Rosa Parks, buses can't have "Black Only" sections in the back. A restaurant can't have "White Only" entrances, lunch counters or drinking fountains. It always was unconstitutional and is now recognized as not legal.
IANAL, But until someone who is can improve my understanding, it would seem that "Your House, Your Rules" in this case is quite polite but not constitutional as the rules in this 'house' attempt to discriminate against persons merely exercising their Rights.
I am not expecting the legality of signs like this to magically change of its own accord. But I feel it is important to be consistent as we work to maintain this essential civil right.