What is the religious ruling on canceling congregational prayers at school, and should a teacher resign in protest of this, or comply with the administration's orders?

The preponderant view is that congregational prayer (Salat al-Jama'ah) is obligatory and is not waived except for a legitimate Shar'i excuse. If you are forced to miss the congregation due to the absence of any other source of livelihood, then pray individually. We advise you not to leave teaching at the school, lest it be left open to those hostile to Islam. Work on raising the issue of Dhuhr prayer in congregation during administrative meetings, make it a public issue, and involve your zealous colleagues and the students' guardians, as they have an influence on the administration. Consider your effort as an act for the sake of Allah, and ask Allah for help and steadfastness.