AWS is now and always has been the arbiter of what they allow on their platform. Parler agrees to the terms of service, just like any other AWS customer. Also, providers have to police their customers - they don't want 'wrongful death' lawsuits, for instance.
As for you other concerns, the conventional wisdom around HN is "Don't build your business on third party infrastructure/services". If they close your account because 'a bad person says nice things' about you, or just because they don't like your face, that's a known risk. There a numerous examples of cloud providers (especially google) shutting down accounts. Its nothing new, and should be accounted for in your business plan.
As for you other concerns, the conventional wisdom around HN is "Don't build your business on third party infrastructure/services". If they close your account because 'a bad person says nice things' about you, or just because they don't like your face, that's a known risk. There a numerous examples of cloud providers (especially google) shutting down accounts. Its nothing new, and should be accounted for in your business plan.