josephstern,
I understand both sides of the issue as well, but I base my food decisions on this.... a place that takes some sort of reward program from me gets the nod for a first visit. The quality of the food and unique environment makes me return. If you don't have access to my preferred payment, you lose out on the marketing capabilities to reach me on my first visit.
If a small business owner does not see the value of accepting a customer's preferred payment method, then they should not expect that customer to return. Someone said it is 10 times more difficult to get a new customer than to retain one, right?