Yes, anyone can become their own domain registrar if need be.
As for credit card processing services, generally Visa and Mastercard are enforcing policies of the banks that actually provide the credit; they simply take the heat because they're paid to. But on that note, both the CEOs of Visa and Mastercard are...Republican donors...almost exclusively...and so would, if anything, favor right-leaning websites such as OAN.
I don't actually know who you're referring to, either on the comedian side or the "you know who" side) but if you're referring to Kathy Griffith she is gainfully employed in Hollywood again and was never banned by Visa or Mastercard. She simply lost a bunch of gigs because people didn't want to be associated with someone who thought it was funny to joke about beheading the president (regardless of whether they agreed with her sentiments).
And becoming a domain registrar requires a demonstration of technical capabilities, but otherwise does not require any privileges. Literally anyone can apply to become a domain registrar if they can demonstrate that they actually know how to do it.
OAN spread falsehoods, not information. If they choose to spread falsehoods, they're free to do so on their own website, but they don't have free reign to do so on someone else's website.
(If they want to prove that their claims are correct in the fact of everyone else saying they are wrong, the burden is on them to prove their claims, which they didn't even bother to do. They just claimed that something is a cure for COVID without evidence, and provided an affiliate link to a website where you could buy the supposed cure. That's not reporting, that's advertising.)