DJ Jyn would totally be into Avril Lavigne, P!nk, that kinda of punk music stuff. DJ Cass would totally remix the classics. DJ Kay would be so into electronica. I dunno about the others.
I agree with Jyn and the punk, though I also imagine her spinning lots of British rock and Icelandic alt rock mixed with said punk and then the occasional British 80s and 90s pop (Steps, Take That, Wham!) to throw people off. For the rest of them, I imagine Cassian would spend time pouring over his mixes–infusing a lot of jazz (Miles Davis Sketches of Spain in particular and some Donald Byrd) and world music–subway salsa, Ethiopiques, and Fela Kuti with whatever is almost quite popular but isn’t mainstream so that it is both familiar and unfamiliar. Kay plays ambient music and refuses all requests. Sometimes he just puts on a record that consists of the sound of rattling chains. Bodhi is basically Riz (lots of hip hop influences), Chirrut is really into trance, and Baze plays house music but everything is overlayed with music performed on a guzheng.