No, those companies don't have first amendment rights. Commercial speech has always been more limited than personal speech. If the law worked like you claim, common carrier laws for railroads would be unconstitutional because they'd violate railroad company freedom of association. These laws are, in fact, constitutional, and so will be the laws that stop big tech censorship.
Besides: corporations? Rights? Total bullshit. This country ought to be run for the benefit of its citizens, not abstract entities like big tech companies. A corporation is an artificial construct that can exist only because society --- made up of humans --- determines that the corporation is in society's best interest. When a corporation is no longer in the best interest of the humans that make up the world, screw the corporation.
How? Create a cause of action whereby if a tech company removes someone's content, that person can go to court and ask that a judge determine whether that content removal is some kind of anti-spam operation or viewpoint censorship. You don't let the company have the final say.