It is an analogy, and it's already established we aren't discussing law. The question is the principles, causes, and reasons at play and how they relate to other principles, causes, and reasons.
I think it would be helpful to forget about the "Republicans" and think about other people who might hold other opinions which may not be shared by the owners of one of the dominant platforms for announcing your views.
No one is saying that New York Times has to publish the story. However, if someone wants to publish a story and announce it to their followers on a platform, citizens need to think long and hard before agreeing to "whatever the shareholders want goes."
The fact that they do not have a product they sell to the recipients of information at a positive price makes it harder for competitive alternatives to gain any traction at all. So, the fact that once a platform like this achieves a certain reach it is unlikely to be effectively challenged means we need to think hard about how much power we want them to have in terms of shaping the conversation: Both conversation we like and conversation we do not like ... It is not sufficient to think in terms of your affinity to the dominant forces. You have to think about what kind of society you want to be in when you are in the minority.