How can a library allow patrons to use a CD-RW for data disks but prevent them from burning music?

It's all about copyright laws. This is just a shot in the dark, but perhaps the RIAA has come down hard on libraries for allowing music to be copied, so they try harder to enforce that. Data discs, on the other hand, maybe there's no one trying to enforce the protection of them, so librarians turn a blind eye. It's probably technically not allowed either way, since those are in most cases probably copyrighted materials. Bottom line: You do not have the legal right to burn copies of copyrighted material, unless you own the original and are making a backup. So if you want to burn copies of anything from the library, you'd better rent it and take it home where there's no librarian looking over your shoulder.