Precisely. What some people want is for some judicial process to interpose itself in collusion between a private company and the government against the interest

Precisely. What some people want is for some judicial process to interpose itself in collusion between a private company and the government against the interests of individual clients of a private company... That if the Executive says "jump" and a private company says "how high?" in violation of no particular statute, the judiciary would stop them for First Amendment reasons. It won't, because the companies don't own a private citizen's First Amendment right.