That is essentially the novel legal theory behind Donald Trump's lawsuit against several social media companies. He claims that by following federal government censorship requests they are essentially acting as an arm of the government, and thus users should be entitled to 1st Amendment free speech protections. There is no case law to support Trump's claim so I expect he will lose, but I guess we'll see.

https://www.npr.org/2021/07/07/1013760153/donald-trump-says-...