I dislike going anywhere I do not feel wanted. Fortunately, we have plenty of competition in the denver metro area. I go elsewhere after raising a stink. Sure it is their perogative as it is mine to take my money wherever I choose.
Rarely do I ever encounter this issue. The first time I went into REI carrying my pannier, I asked the greeter if they minded. The response was "feel free to take it in. If you do not want to carry it around we have lockers to put it in". Well, I think it was lockers. My horrible memory is kicking in. Good place.
Plus, many women carry huge purses. Carrying one pannier around looks like a large man purse.