Praise be to Allah.
The shar’i ruling differs depending on the state of the school referred to in the question.
If it is a religious school, in the sense that it was established to produce priests, monks and nuns, and it is working to establish a new generation of this class of people, then we do not think that you should work there, and we can only advise you to be cautious and to keep away from it, even if you are being called to teach other, secular subjects, because by taking part in working with them you will become part of their institution, and it is as if you are helping them in their kufr which they want to teach to the children.
But if it is an ordinary government school, but has a Christian administration that wants to teach the Bible, and it is limited to that, then in that case there is nothing wrong with you working there and becoming part of the faculty, so long as you adhere to the commands of Allaah and observe proper Islamic hijab, and perform all acts of worship on time, and have a good attitude and treat others well, and avoid forbidden things, one of the most serious of which is loving the kuffaar, feeling comfortable with them and imitating them.
When working with them, you should be keen to spread the truth and call people to it, and rid whoever you can of the darkness of ignorance and shirk. But if the school requires you to do any Christian acts of worship or traditions, or it is mixed (men and women together), or you fear that you may be dazzled by specious arguments as the result of mixing with the Christians, then in that case it is not permissible for you to work there, and you should not continue to do so, rather you must leave and shun it for the sake of your religious commitment and so as to protect yourself from falling into the traps that the shaytaan sets for the sons of Adam.
Allaah says (interpretation of the meaning):
“O you who believe! Follow not the footsteps of Shaytaan (Satan). And whosoever follows the footsteps of Shaytaan (Satan), then, verily, he commands Al‑Fahsha’ [i.e. to commit indecency (illegal sexual intercourse)], and Al‑Munkar [disbelief and polytheism (i.e. to do evil and wicked deeds; and to speak or to do what is forbidden in Islam)]. And had it not been for the Grace of Allaah and His Mercy on you, not one of you would ever have been pure from sins. But Allaah purifies (guides to Islam) whom He wills, and Allaah is All‑Hearer, All‑Knower”
We should not forget to point out here the danger of these schools when they are opened in Muslim countries; in that case they are a tool of colonization by stealth, and an obvious means of corruption, concerning which many fatwas have been issued by scholars and academic institutions from the time when they were first established.
And Allaah knows best.