Parler's moderation policies caused their own problems. They decided they wanted to be a platform friendly to violent extremists. Their noted lack of moderation of violent rhetoric, calls to violence, and planning of violence made them a pariah.
Amazon is free to associate with whoever they want. They don't owe service to Parler or anyone else.
And it's not as if you can just go to the social media network down the street. Sites like Parler are trying to be those alternatives, and it's a tough business to even be #2 in.
Higher quality people might not like the seedy pawn shop in that strip mall with all the WW2 memorabilia, but that doesn't mean they shouldn't be able to try to do business.
No part of AWS or Twilio fall under common carrier regulations. They can choose with whom they do business. They would and do cancel service for clients doing illegal things or against their TOS.
Amazon doesn't owe Parler a viable business. Parler made themselves into a toxic environment that drove third parties to abandon them.
Not really. There's not currently any huge controversy about banning spammers, DDoS attacks, or child pornography. A few fringe groups will argue it, but most sensible discussion concedes that censorship is useful and we need limits.