Anthropology is not one of those things that if you didn't do it as an undergraduate, you're sunk. My BA is in English, and I'm working on my phd in Anthro now. There's actually a lot of overlaps between English and anthro and many graduate programs like having students with diverse backgrounds. In the programs I've been in, we have had people with degrees in classics, history, journalism, biology, english, art, pre-law, pre-med, etc.

There are, however, very very few jobs outside of academia (and even then very few), and you'll need more than a Masters. they'll also generally be poorly paid and the degree will take you years and years.