How is it an antitrust case? Amazon doesn't have a monopoly on hosting internet services. And there is no oligopoly for this line of business, there are many thousands of suitable providers worldwide.
It would be different if, say, CenturyLink were blocking content across their transit infrastructure. That would be more like your railroad analogy.
Antitrust legislation isn't built around 100 % monopoly, but rather dominant force and cartel-like behavior, especially if they act to suppress growth of potential competitors. This is the core of antitrust jurisprudence: markets only work in presence of vigorous competition, but big incumbents are highly motivated to obtain so much influence that significant competition does not have a real chance to grow and threaten them.
There is a longish recent staff report on the Web of the Congress regarding behavior of Amazon, Apple, Google and Facebook (almost 500 pages) [0]. I actually read most of it. These platforms have already engaged in a lot of stuff that is anti-competitive. And the latest purge of Parler is, among other effects, also a suppression of a potential competitor.
Of course, the tech giants say that they weren't officially motivated by a desire to suppress a competitor, but they acted against potentially competing firms so many times already that one should be wary about their explanations.
Thanks for clarifying your position, but I still don't quite see how this applies to Parler in terms of their decision to host upon AWS. There are many thousands of other hosting companies worldwide, they didn't have to use one of the big three IaaS providers.
It seems more like poor planning on their part: over-reliance on specific services of a single provider, and no disaster recovery plan for if this is made unavailable. Particularly considering the business they're in - publishing controversial content that gets its users banned on more mainstream social media sites. They would have been wise to have a backup plan for hosting.
On the other hand, if you were also passing reference to the app store duopoly (as the report mentions this), I agree with you on that. At least on Android a banned app can be fairly easily side-loaded; iOS users are entirely subject to Apple's whims on what their device is permitted to run.
I could definitely have formulated my opinion better...
If Amazon acted alone, I do not think that there would be an antitrust case. But given that Amazon acted together with the app store duopoly, in what appears to be a coordinated action with the same goal, I think the antitrust case applies. If two very dominant players make a pact with a third not-so-dominant player to squeeze somebody a bit more, it only makes their anti-competitive behavior harsher.
BTW, I believe that Parler really could have prepared better. It is obvious that they did not have a good plan B.
Why do you assume that there was necessarily coordination? In my opinion it's likely everyone who is dropping Parler came to their verdict independently.
It is certainly possible that they all acted independently, but given how many cases of anti-competitive behavior on their part have been documented in the linked report of the Congress - these companies are not completely honest.
Mikhail Gorbachev used to say "Trust, but verify." I would like to see some verification in this case.
It would be different if, say, CenturyLink were blocking content across their transit infrastructure. That would be more like your railroad analogy.