If they didn't like the AWS terms of service, they shouldn't have entered a contract with them to abide by those TOS and use the services.  Based on the below, AWS also gave them warnings to come into compliance, which Parler did not do.

(Perhaps there is room in the contract language where the TOS aren't super-clear which could play out in a legal challenge, but this is not about just "silencing conservative voices."  It's about what AWS is claiming is a breach of contract by Parler.  If one party breaches a contract, the other party can discontinue services.)

Here is the letter from AWS to Parler:

Dear Amy,

Thank you for speaking with us earlier today.

As we discussed on the phone yesterday and this morning, we remain troubled by the repeated violations of our terms of service. Over the past several weeks, we’ve reported 98 examples to Parler of posts that clearly encourage and incite violence. Here are a few examples below from the ones we’ve sent previously: [See images above.]

Recently, we’ve seen a steady increase in this violent content on your website, all of which violates our terms. It’s clear that Parler does not have an effective process to comply with the AWS terms of service. It also seems that Parler is still trying to determine its position on content moderation. You remove some violent content when contacted by us or others, but not always with urgency. Your CEO recently stated publicly that he doesn’t “feel responsible for any of this, and neither should the platform.” This morning, you shared that you have a plan to more proactively moderate violent content, but plan to do so manually with volunteers. It’s our view that this nascent plan to use volunteers to promptly identify and remove dangerous content will not work in light of the rapidly growing number of violent posts. This is further demonstrated by the fact that you still have not taken down much of the content that we’ve sent you. Given the unfortunate events that transpired this past week in Washington, D.C., there is serious risk that this type of content will further incite violence.

AWS provides technology and services to customers across the political spectrum, and we continue to respect Parler’s right to determine for itself what content it will allow on its site. However, we cannot provide services to a customer that is unable to effectively identify and remove content that encourages or incites violence against others. Because Parler cannot comply with our terms of service and poses a very real risk to public safety, we plan to suspend Parler’s account effective Sunday, January 10th, at 11:59PM PST. We will ensure that all of your data is preserved for you to migrate to your own servers, and will work with you as best as we can to help your migration.

- AWS Trust & Safety Team