Can you fall in love with no shared interests, only core values?

Relationships are always possible. It's two people sharing deep intimate feelings, it doesn't have to do anything with hobbies, interests or any features.

A white supremacist nazi can still fall in love with a black woman, because it's simply feelings that control love (although not sure if the woman would share these particular feelings..)

The relationship MIGHT be stale but it's doable, and with time you'll find common ground.