In a way yes. Should the utility stop providing electricity because to someone they think I'd using it to manufacture illegal drugs?
I don't think so. The punishment is for a court to decide, not some of their service providers.
Now, arguably, there should be a fallback payment system with utility-like requirements for universal service that can be cutoff only with due process (certainly, that's needed on the consumer side of banking to deal with the problem of the unbanked, but there's arguably good cause of it on the merchant side of financial exchange as well.) For one thing, an explicit guarantee would make it harder for government officers from using informal pressure on private payment processors as a means to punish targets while evading due process, which it has historically done quite often, with the deniability that it is a free decision.
If a person or firm has a reasonable belief that a business partner is committing crimes or even just behaving unethically, I would say they have an obligation to curb the activity or end the business relationship.
This idea that only the courts should limit or punish crimes pops up here once in a while and I've always found it bizarre.
If child porn was not a crime would you be ok with Visa and MasterCard doing something then? Is it in your view that should they only not do something because it's a crime?
Isn't that the entire point of a court? to have a monopoly on punishing crimes so that people aren't unfairly punished on the basis of gossip or false allegation and so that society doesn't sink into a cycle of vengence where one group punishes the other group for their punishment, and so forth.
That said, punishing a crime is different from refusing to do business with someone because you don't like them. I think the objection is that payment processors are an oligopoly which gives them too much power to behave arbitrarily. If you live in a city and one grocery store doesn't do business with you, that's fine go somewhere else. If there is only one grocery store, then that's akin to starving someone and it should require the evidentiary standard of wrong doing a court would have.
The courts do have a monopoly on certain types of punishment, like prison. Other, informal types, such as declining to do business with somebody, are available to individuals and companies. I don't see that as a contradictory or undesirable situation.