No, that's not the same at all. MasterCard could report PornHub to the police and still keep them as a customer. The police (well, FBI, probably) could decide what to do from there. They might investigate and find that PH isn't violating any laws. Or maybe they are, and get fined or some of their employees prosecuted. Either way, "this company is doing crimes" should have nothing to do with whether or not they can be MasterCard's customer.

(Ignoring, for a second, KYC-type laws that can make MC criminally liable for not policing their own platform... laws I think are mostly garbage.)

Your analogy doesn't fit, because the current scenario (MC kicking PH off their platform) would be like if a daycare discovered criminal activity involving one of the kids they watch and then refused to watch the kid anymore. (Which would be a bad thing that might make the kid less safe!)

Doesn't a business have the right to decide who they get to do business with? If a business sees a customer doing something they're not comfortable with, don't they have a right to refuse service?

They do, but once you are a certain size, decision you make, create much bigger waves. At that point, 'derisking'(as the banks call it ), can easily alter the economy in unpredictable ways. This is one of the reasons, you typically do not want monopoly/oligopoly in place. MC and VISA already have amazing amount of market power. If they say they won't process your payment, you only have few options left ( wikileaks donations debacle comes to mind ).

We need to distinguish between institutions so big that they are defacto system and institutions that are mere cogs of the system.

Your argument is a good one, but it ignores attributes of the parties.

Another example. If you tell anyone at a school (public or private) or a psychiatric professional that you have intent to harm yourself or others they are also required to report it.

They're required to report it, not expel you from school.

MasterCard could similarly report these alleged (alleged!) crimes, while still processing their payments, and avoid damaging someone's business without due process.