Whereas AWS can plausibly claim that they don't want to host illegal content, what can Twilio say for themselves here? From Twilios perspective, providing Twilio's core product to Parler isn't any different than serving them to other platforms. They have no responsibility or liability. The lack of moderation on Parler is irrelevant when Twilio isn't involved with moving that data.

For a Saas platform to abruptly cut-up a contract, immediately breaking the authentication mechanism for the site on the other end of the contract, which directly results in a serious data breach for thousands of users (the majority of which have done nothing wrong), because your employees and leadership don't like their politics, doesn't sound like something that a publicly traded company should engage in.

edit: especially once it became obvious that AWS was going to bring the site down just a few hours later. They had a clear route to make their ideological stand and cause no damage by merely waiting 12 hours more.