It's not on a whim.
Payment processors -- including Visa, Amex, Discover, Mastercard -- have clear rules about hate sites and promoting violence. This is a rule clearly spelled out that all merchants must follow.
Infowars violates rules they agreed to follow when they became a merchant. That's breach of contract.
Edit: and here's Paypals AUP: https://www.paypal.com/us/webapps/mpp/ua/acceptableuse-full
You may not use the PayPal service for activities that: ... relate to transactions involving ... the promotion of hate, violence, racial or other forms of intolerance that is discriminatory
Seriously... that's breach of contract. Does infowars need to follow the contracts they agree to? Do those that promote hate get to disregard contracts?
Peddling hate speech does not earn you the ability to disregard contracts you have agreed to.