The payment providers get to charge a 2% fee on all transactions, without any pesky questions about antitrust law.
In exchange, when politicians ask nicely, the payment provider cuts folks Wikileaks, out of the financial system without any pesky questions about the first amendment.
So this results in websites that allow people to upload pornography having lapses of moderation where something bad gets through every now and then. One day some creepy clip goes viral among some social conservatives and they try to make legal threats against the site and anyone they consider "affiliated". This creates problems, credit card companies are very protective of their reputations, and they usually decide the conservatives seem less bad.
Then someone sets up a new site that allows user-generated adult content and the cycle repeats.
Merchants that sell porn, gambling, and other vice have higher rates of fraud. If they allow them to accept credit cards at all, they charge them much higher merchant’s fees to do so.
This is one of those situations where the optimal level of fraud isn’t zero.
Do the credit card companies go to Wal-Mart, find all the fraud is people buying cigarettes, spirits and razor blades, and tell Wal-Mart to stop stocking those?
Of course they don't.