From my perspective, it's clear that the producers chose her in the competition not only for her voice, but specifically because she's religious. The issue comes up during her first tryout, and the words that they use to describe her singing ("pure", "modest") are clearly influenced by this issue. They even ask her to sing piyyut, which she gladly does.
Her appearance obviously raised the challenging question of how to respond when a member of the religious community does something that contradicts the values of Jewish law. (And her singing publicly clearly does violate halachah according to the vast, vast majority of poskim, despite arguments to the contrary. This episode reminds me of when the Maimonides grad who participated in a modeling reality show.)
How should her school - a religious Ulpana react? Educational institutions are not charged with policing the actions of their students, nor should they be. But when a student publicly acts in a manner that clearly contradicts the values of the school, she becomes a de-facto spokesperson and representative of that school. Other parents rightly or wrongly begin to wonder: "Really, that's how students at that school act? Maybe it's not the best place for my daughter." (We might not like it, but that is how things work). In this case, the school struggled mightily with this tension, and in the end the student agreed to leave school for two weeks voluntarily, allowing the school to express its displeasure with her performing without officially punishing her.
What about her rabbi? How should he conduct himself throughout the episode?
In my prep for the class, I came across a fascinating article describing what happened when the film crew came to the girl's yishuv to film hoping to conduct a joint interview with the rav of the Yishuv, Rav Zvi Arnon.
Rav Arnon refused to speak on camera, even after the camera crew literally ambushed him at shul during minchah. He explained his refusal by saying that no matter what he said, he would be portrayed as a villain, specifically because he represents a viewpoint that's against the underlying values of the entire television show.
Fascinatingly, the members of his community (a religious community), rather than supporting him, were angry with him for failing to support the budding television star.
The article raises fascinating and important rabbinic issues, including:
1. Dealing with a media hostile to religious values
2. Dealing with ba'alei batim who don't support a halachic viewpoint
3. Representing a Torah point of view unpopular in a modern Orthodox community
4. Interactions between religious and non-religious Jews: In her tryout, three different mentors vied for her to choose them, one of whom clearly had religious tendencies. She chose Aviv Gefen, apparently the most secular of the three. Is that something we should try to discourage? The clip I shared above is her visit with him to the shul in Nir Galim, as they talk about religion and faith. Can you create a Kiddush Hashem in the context of a larger violation of Jewish law?
5. Finally, why don't Modern Orthodox Jews, by and large, adhere to or seem to care about the halachot of kol isha?
Personally, I believe that Rav Arnon made absolutely the right choice. He found himself in a lose-lose situation, over which he'd have no control. But it cannot be easy to be the representative of an unpopular Torah value without even the support of the members of your own community.