If you're in the UK there is a parliament.uk petition to "Ban payment processors stopping services based on objections to legal content": https://petition.parliament.uk/petitions/734441
The reason these credit card companies wield so much power is the modern duopolistic system. "Monopolies are ILLEGAL" they said. Thusly, an array of duopolistic megacorps essentially acting as a monopoly. Something something game theory. Visa and mastercard. Coke and Pepsi. iPhone and Android. Windows and MacOS. Google search and google search. NASDAQ and NYSE.
The answer is to have 10+ actually competing, financially healthy payment processors. At some point the cabal-like duopolistic behavior breaks down.