> The first amendment protects you from censorship by the government
It is assumed by the 1st amendment that we have freedom of speech (among many other rights). The amendment does not grant the right, but prevents infringement of it.
At the time of the amendment, there was concern that the federal government might infringe on it, so this amendment specifically called that out.
Later, it became clear that the states had a history of infringing on these and other rights. We fought the Civil War over this. The result was that now states are also enjoined to not infringe on these rights.
Later, it became clear the corporations might infringe on the rights of people, as they, too, were becoming very powerful. This was the anti trust era. It's pretty much settled law that when a corporation attains a certain level of power, as indicated by monopoly status, then they are restricted in their activities. We do not allow the electrical monopoly to cut off power to groups they don't like, or force the signing of terms of partisan terms of service.
Later, during the Civil Rights era, segregationists insisted that people didn't have a constitutional right to eat in the restaurant of their choice, use the drinking fountain of their choice, go to the same schools as others, etc. The federal government ended up sending in the national guard.
These private businesses don't get to infringe on rights just because they're private.
So, the 1st amendment has not only broadened, it has also put the federal government in a sort of supervisory role to interfere when it sees states and business infringing on people's rights.
There is nothing special about a social media company that should give them the ability to infringe on our rights.