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Parler's CEO was interviewed by Megyn Kelly on her podcast a couple days ago, and if what he said is true, AWS is not being truthful. Of course we don't know who is telling the truth, but Parler is asking to release all the correspondence between the two companies, and AWS will not consent. It could very well just be standard legal best practice (since there is a lawsuit in progress), but it does give Parler some credibility. As soon as there is evidence I will re-evaluate where I can stand (not that it matters of course, but to me personally it does :-)
I don't think this adds to Parler's credibility. I'd say it's consistent with their self-portrayal as the innocent victim of a liberal conspiracy.
Parler's moderators were fine with content like https://i.redd.it/om90nwadqca61.png - it's not surprising that Apple, AWS, and Google found it unacceptable.
Making these emails public (even in a censored form) could expose AWS employees to doxxing, harassment, and worse. An email system administrator, for example, could use the text of an emails to identify which AWS employees corresponded with Parler.