You accept the payment, absolutely. It should not be your responsibility to do the required due process to ensure that a decision to deny the transaction is actually fair and correct. And more than that, I don't want to have to trust an unaccountable private corporation with that responsibility.
So it should be illegal to start a vegan payment processor? Breaking up the current near-monopoly and giving you more choice would give the maximum possible freedom to everyone including you.
> unaccountable private corporation with that responsibility.
That's the beauty of a functioning market. With lots of choice the corporation must either be accountable or lose your business. The real problem is that you currently don't have much choice due to a non-existent market with almost no real competition for business.