Yes, it is a Free Speech issue.
Her disagreement with Moore had nothing to do with her performance in the pageant. She was stating her opinion which we as Americans have a right to do.
If she had done it during her performance, the people who now run the Miss Universe pageant could take action. But this was totally removed from the show. Any American who holds a job would be denied free speech under your logic.
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.