This is not true. It's quite a complicated topic that SCOTUS still has to fully adjudicate[1]. Regardless of what side you land on, the argument that "moderating user content on themselves is not an infringement of the users free speech rights" is not straightforward, given current legal debate[2][3].
The main issue is that there seem to be two competing claims to the First Amendment: users expressing their views on what some might deem the new "digital public square," and social media companies having the right to allow (or disallow) certain content on their private platforms.