Everyone on L&D at the hospital I rotated at (including the RN students and paramedic students) were issued the same dark blue scrubs as everyone else. Name tags? No one reads name tags. The major difference, however, was the medical student name tags were facility name tags, unlike the RN student and paramedic student's name tags. However everyone also had access to the c-section surgical suites. Granted, the RN students and paramedic students weren't going to scrub, but as long as it wasn't packed (normally wasn't, but it gets a little crowed between an attending, resident, med student, surgical tech student all being scrubbed with a surgical tech supervising the student, a circulating nurse, and a RN student watching, which happened a few days).
I think the bigger issue is attitude. I never got a "I don't want a student doing my pap smear/pelvic exam/wet mount" when I was doing OB/Gyn. I got a handful of the "I'd rather have a female," but even those were generally fine with a female student. However it was always a, "So... we need to do a ___" and not a "would you mind if I did a ____."
