I agree with your view of PayPal's proper role, but as a private business, if they want to choose not to do business with neo-nazis and ilk, that's entirely within their legal rights, and many would say it's morally justifiable too.
What I take issue with more than anything else is the idea of a private business expropriating money from people based on the contents of their speech, as a change of contractual policy, buried deep in the terms of service, that many laypeople cannot be reasonably expected to read and comprehensively understand.
I'm also concerned about this policy being weaponized by bad actors. Say someone impersonates a PayPal user online and posts genuine hate speech, complete with calls to violence. Or someone sends a payment to an innocent PayPal user with a memo that implies the PayPal user was engaged in hateful or malicious conduct. What happens when someone is having a mental health crisis and says some awful things on Twitter due to genuine mental health issues? What happens if a PayPal user's online account on another platform is hacked and used to post hateful content? What safeguards are in place to ensure that only those who are actually guilty are financially penalized?