My husband knew what a 401k was but didn't start investing in his until I talked him into it, when we were dating. However, while being rather laissez faire about money management, he's an excellent earner, and he's not a big spender. I think these two qualities are more important than expertise in money management. I manage the family money and investments now, which I don't mind.
I would break up with her if:
1.) She has credit card debt
2.) She's incapable of earning a decent living and you don't want to financially support her