not normally in meatspace, no. here online, they have more power.
these payment processor cannot deny the sale of a porno mag bought at a convenience store, for example.
they also have no issue with processing payments for strip clubs and "adult shops" in meatspace.
it is really /only/ online that they have so much power. i suspect that some portion of this stems from the fact we're dealing directly with the credit company, and not the intermediaries usually found in meatspace.
using my convenience store example, none of those have direct dealings with the credit companies, they all go through intermediaries like veriphone. even using your debit card goes through your bank instead of the credit company directly.