Never accept a caution without taking legal advice, and never ever accept one if you believe you are not guilty. A 'simple caution' is an admission of guilt, and can stay on your record indefinitely in some cases.
Anyway, a ban of this sort has no legal basis, other than in the fact that a shop is private property, so the owners can refuse admission to pretty much anyone they want to. There are other golf shops, and to avoid embarrassment it migh be better if your friend used one of them.