>>27500841. Rei is a teenage girl, so her taste in music is automatically awful
2. Judging from her poem in episode 14, Rei is concerned with existential questions
3. Rei is suicidally depressed but also unusually tough following bushido
4. Rei reads incredibly weird shit not even in her native tongue
5. Rei is pretty dedicated to her man
Therefore, Rei will listen to music that's quite sad and melodramatic, where men and grills love and die for each other, and that has some intellectual quotes for her to chew on.
You can't argue against this logic.