Consider for a second if some political position was banned by all privately owned mediums in the US. Say for example it was reported on the violence is Bangladesh. Every internet provider would stop transferring data if it detected any mention of it, every server hosting data in any format would immediately remove any mention of it, Microsoft, Google, and Apple pushed updates to their OS's that would terminate what you were doing if they detected it.
Would freedom of speech (not the First Amendment) have been attacked in such a far-fetched scenario? Yes, despite it only being private companies doing things they have the right to do. As such, we can conclude that in such a scenario, freedom of speech includes requiring private entities to support a message they wish to not support. Now, would that not also apply in a less far-fetched scenario? I see no reason it would not.