The First Amendment is not the same thing as Freedom of Speech. Freedom of Speech is an ideal from Ancient Greece and obviously predates the US Constitution. It’s also much broader in scope.
So, yes, people can have their freedom of speech infringed by a private company or employer, even if it’s not protected by the First Amendment.
So, yes, people can have their freedom of speech infringed by a private company or employer, even if it’s not protected by the First Amendment.