Q. What do Jewish teachings say about the way in which Jews should interact with non-Jews?
It is obvious from the Mishnah tractate Avodah Zarah that there was considerable contact with non-Jews, but at the same time Jews were warned not to get involved in their idolatrous ways.
The Jew had to behave morally to a gentile, supporting their poor, visiting their sick, burying their dead, etc. (Gittin 61a), but Jews had bitter experience of the cruelty and immorality of the gentiles.
This began in the days when gentiles were heathens, but even – indeed especially – under monotheistic faiths Jews suffered from gentile hostility and developed an inbuilt suspicion of the gentile.
Nonetheless Maimonides and other authoritative writers insist on Jews treating gentiles with respect and honouring Christians and Muslims for their monotheism.