Evidence and due process are important for convicting someone of a crime. You're not violating a basic human right when you deny a credit card transaction. The requirement for evidence and due process should be far lower, if even needed at all.
This doesn’t work when it’s something basic like payment processing. It’s the same reason we decided as a society that people can’t “trust their gut” and deny housing to people based on the color of their skin.
Running a profitable online business is not even a basic human right. No one owes you payment processing. Forcing someone to be a supplier to a hate group violates their basic human rights. If payment processors were discriminating against a protected class such as race or age then you might have a point.