It depends on the relationship and the people involved, but I find that common goals and values matter more than interests.
I'm not a meat eater, my husband is.
I'm very social and would rather go out, he's not social at all and would prefer to stay home.
We never agree on movies, TV (I rarely watch it) and music.
He loves working in the yard, I'd live in a condo to avoid yardwork
He loves the beach, I prefer the mountains
He's very much a type A, list making, organized control freak and I just go along my merry way most of the times. That actually works for us because he keeps this household running most days (but I'd never admit that to him...lol).
The list goes on and on and on....
However, we indulge in a favorite past time with eachother pretty frequently. Sometimes it's fun to shoot off rockets in an open field or watch football on TV (now if it's hockey, I'm all for it!). It's not something I would have ever said "YES...I MUST do this in my life" but it's fun when I'm with him.
As for the food issues, it's not really an issue at all. I cook meat, I just don't eat red meat or pork. I don't cook an entirely different meal for myself. I have leftovers or I just eat the sides or I'll get myself a piece of salmon when I feed everyone else filet. Not a big deal at all. I can never understand people who think this will be the be-all, end-all to a relationship.
We both have common goals and values though, which seems to keep things ticking.
I will say this...I don't like to be suffocated. There is such a thing as "too much together time" and I will never be the type of person that needs to be around my husband (or anyone) 24/7 so maybe those shared interests don't really matter all that much for us.