Earlier quoted context omitted.
The content is hosted on a computer owned by a corporation, not the government. Many people interpret this as their decision to make, rather than the government's. If you don't believe so, you'll have to describe the ways in which their rights to their computers differ from yours.
See my response here, I believe that's also relevant to your question: https://news.ycombinator.com/item?id=25764333
In short, Amazon is not a public utility. Maybe it could be in the future but it isn't right now. AWS is a private business which rents out a server under very clearly laid out TOS to follow. In addition to this, AWS has gone out of their way for weeks (if not months) to work with Parler on their moderation issue that violates the contract.
Parler has shown no intent to work within the boundaries of AWS TOS. Instead of putting in the work of finding and migrating to other hosting solutions (of which there are many) they used stall tactics. When stalling no longer worked, they brought a junk lawsuit against AWS.