It is not a government agency and our Bill of Rights has nothing to do with this. It is a private corporation, and, as such, cannot be held to the Constitution. These are not government workers. A private organization can ban or disqualify for any reason because it is not owned by the government or funded by it. I don’t see why you don’t understand this.
In fact, the pageant is apparently owned by Trump. Furthermore, it is not a job—it is a scholarship program. This has nothing to do with employment or employment discrimination. They can ban these contestants for doing sex tapes, which, according to the SCOTUS, is free speech, so why can they disqualify contestants for that, but not for saying something that the people running the pageant don’t like? You act like she was thrown in jail or something and not disqualified from a stupid beauty contest. As I said, I don’t agree, but you can hardly walk into court and say that a private organization that has nothing to do with the government infringed upon your first amendment rights. The Founders wrote the Constitution to limit the government—not beauty contests.
“the pageant is apparently owned by Trump”
The pageant is no longer owned by Trump. He sold it and commented that if he still ran it the screw ups like announcing the wrong winner would not have happened.
The contest has rules. If she violated one of the rules then they can take action. I don’t see how she did but I am not familiar with them all.
Her disagreeing with Moore had nothing to do with the pageant. She earned her right to compete. The sex tapes example you gave is not the same because these events have morals clauses for the contestants.