Listening to Christian music is downright forbidden, and listening to non-Jewish music in general is within a spectrum of being muttar, to frowned upon, to assur depending on the community and halachic authority.
If one is on a job in which the other workers insist on playing Christian/non-Jewish music, and even after respectively asking to have it turned off they will not listen, what should the Jew do? Is he allowed to work with the music playing in the background, as long as he makes sure not to derive or show pleasure from it? If he wears earplugs to muffle the music would that change anything? Would be required to quit the job and work elsewhere?
If one is in a situation that they have no choice other than to listen to Christian music, he should do what he can not to listen to the music. If after asking them they don’t listen, as you are saying, maybe try listening to Jewish music on an MP3, or to a shiur. This will surely drown out the noise of the music. Earplugs as you mention are also a good idea. You do not have to quit your job because of it, because you are not listening to it because you want to. Therefore you are not doing something that is assur, however try doing whatever id possible to block out the noise.