I'm pretty sure companies in the 1960s South didn't want to serve black Americans.
In fact, many want the Government to go further and force bakers to make cakes for gay weddings when the owners don't support gay marriage [1]
[1] https://www.abc.net.au/news/2018-06-05/court-sides-with-colo...
What is a protected class could be expanded and the Government can force everyone to do business with unsavoury types.
If making and receiving payments is considered a necessary utility posting and handling large amounts of cash is restricted, then providers should not have a right to deny service to customers who are not taking payments in violation of the law, regardless of distasteful their activities may be.
Would you agree if the state sided with electrical or water utilities to be able to refuse service to a customer such as brothel, on the grounds that their activitites where distasteful and immoral, not matter how legal?
That would be fine if the person denied service had the right to connect to a river or a well, lay down their own pipes and power and draw their water and electricity directly, but those rights are curtailed by the state, and it requires certain permissions and rights to do those.
The same can be said of online payments and credit card payments. They have become a necessary utility so much so that brothels and panhandlers have credit card machines. If private providers can deny such service arbitrarily then the state must become the providers of last resort.
if private processors can deny service for no reason
Ah yes, the "no reason" of being violence-inciting Nazis. What a reasonless judgement.
Do you see a reason stated in the termination notice?