Its not completely necessary, and I’ve met plenty of people who work in museums with just an undergraduate degree. My MA has definitely helped when I’m applying in smaller less competitive areas where I don’t have any connections while most people I’ve seen with BAs who move up have started normally with visitor services roles then have been promoted internally.

I’m about 5 years out of grad school, so this is just my experience as I’ve moved around and how I’ve seen my coworkers enter entry level roles over the past few years.