Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Answering your question, Sheikh Mustafa Umar, President of California Islamic University, states:
The general rule when it comes to working in a place like this is to ensure that you are not promoting anything that is against the teachings of Islam.
The situation, as you have described, seems pretty clear that this job is fine because you are not promoting or encouraging the Christian religion, especially since most of these students chose to attend a Christian University in the first place.
Your situation is completely different from someone who is selling and promoting Christian missionary literature in a mall, for example. So it is fine for you to work as a librarian in a Christian university.
Almighty Allah knows best.