This is a public school so they are considered a part of (subsidized by) the government. But if it were a private Christian religious school, and she was promoting Satan worship in her out of school TikTok time, would you think the school should be forced to ignore it and let her keep singing in their televised choir?

Hmmm, I'm not sure that's the meaning of free speech. Forcing a private entity to provide an unpaid service is something quite different.