First amendment apply to the government and anything that functions equivalent to the government. Its that second part that court has made decisions going both way, and the question got mentioned as recently as this year when Trump twitter account got declared to function equivalent as any other official government forum. In that specific case the twitter account of the US president was deemed such, but the whole of twitter was explicitly not judged on.

Beside that, a lot of people talk to media about first amendment they often then go to court raising anti-discrimination laws. Those laws are much more broader and can be applied to private funded companies. When it comes to international companies there is also free speech as defined by the EU and that one do not make a distinction between company and state in the same way as the first amendment. The distinction between free speech (US first amendment), free speech (EU human rights) and free speech (US anti-discrimination) are all fine legal technicallities, but limitation in one does not give private funded social networks free range to do whatever they want.