How did he mess up? How is this different from if he had emailed a critical letter to the local newspaper? Teachers have a right to do these things and not be fired. I haven’t listened to the song; is it obscene? Racist? If not, then this school maybe opening itself up to legal trouble.
No, the teacher does not have a right to do these things and not be fired. They are either contract employees or union employees. They can be fired by having their contracts terminated or via union proceses.