My sister has a masters degree with honors in museum science and was never able to get fulltime work in a museum. To become a curator, connections are key, specifically connections to the museum’s principal donors. Wealthy patrons always have a relative interested in museum entry level positions and the clout to see that they are hired. You can’t work your way up to curator without getting your foot in the door, and there’s often someone with more expensive shoes in line ahead of you.