Here is one example of a med school’s preference in applicants:
UC Davis’ admissions office, Dr. Fancher said, doesn’t give more weight to one major or another as long as a student has completed the required prerequisites. “We look for mastery in an area that a student is passionate about,” Dr. Fancher said. “That could be in the study of art or history or science, in participation in college athletics or music or dance, or in making an impact in their community.”
This attitude is held at other types of post grad schools and jobs as well. Of course, GRE, LSAT, MCAT are all important factors as well in admission.
For jobs after getting a BM, it might help you to talk with a conservatory or school of music and ask them what grads end up doing. I think it would be reassuring.