"The ability of companies such as Facebook, Twitter and Google to control what people see online is so potent, it is the subject of antitrust hearings...."

"But the decision by Amazon to push Parler off its dominant cloud-computing service illustrates just how powerful its content-moderation capabilities are as well.... [T]he companies that provide the technical infrastructure that powers websites and services where people express opinions have vast power as well, though they rarely use it. They include little-known companies that register website domains for customers; so-called content delivery networks, which can boost the speed at which webpages load; and Internet service providers, which connect homes and businesses to the Web.... [Amazon's] Amazon Web Services is the dominant provider of cloud infrastructure services, which let customers rent data storage and processing capabilities over the Web instead of running their own data centers.... [AWS's] Trust & Safety team, which has fewer than 100 workers, acts only on complaints received. In its reply to Parler’s suit, Amazon said it received reports in mid-November that the social network was 'hosting content threatening violence.'... It accused Amazon of conspiring with Twitter to take the smaller competitor offline just as it was significantly gaining users in the wake of Twitter permanently banning Trump.... 'Without AWS, Parler is finished as it has no way to get online.'" 

WaPo reports.

Here's the top-rated comment at WaPo: "If you support a baker choosing to not selling a wedding cake to a same-sex couple, then it follows you must support a company choosing not to do business with a customer that behaves in a manner contrary to the company's known parameters. As the same-sex couple was told, go find someone else to bake your cake. Parler should do the same. If they can't, perhaps it's the 'cake' they are trying to bake."

IN THE COMMENTS: MayBee takes on the cake analogy:

Parler was already on AWS. 

So the baker (aside from scale, monopoly considerations, and anti trust issues) situation would have to be more like: 

The gay couple hired the baker, paid the baker, and then on the day of the wedding the baker refused to deliver the cake. The baker, however, delivered a lot of cakes to your ex-boyfriends wedding on the same day. And then the baker announced you were dangerous.

"Hours after it went offline on Monday, the social media start-up Parler filed a lawsuit in federal court accusing Amazon of violating antitrust law..."

"... and asking for a temporary restraining order to prevent the tech giant from blocking access to cloud computing services. Amazon told Parler over the weekend that it would shut off service because 'a steady increase in violent content' on the site showed that the company did not have a reliable process to prevent it from violating Amazon’s terms of service. Amazon said it would ensure Parler’s data was preserved so that it could migrate to a new hosting provider. Millions of people turned to Parler after Twitter and Facebook barred President Trump following the riot at the Capitol last week. Apple and Google both kicked Parler out of their app stores at the end of the week, though users who already had downloaded the app could still use it. But the app relied on Amazon’s cloud computing technology to work.... Parler did not provide direct evidence showing Amazon and Twitter coordinated the response. Instead, it pointed to a December news release announcing a multiyear strategic partnership between Amazon and Twitter, and it made references to Twitter’s own challenges policing its content."

The NYT reports.