Can you fall in love with no shared interests, only core values?
I think being able to spend time apart is crucial for any ltr. part of that is having different hobbies. But when you go to the extremity of not having any shared hobbies I think it becomes impossible to maintain a ltr. You'll just become very bored and biter that whenever you suggest doing something together the other person is uninterested or unwilling to do it, and I think on the opposing end, you'd get fed up of pretending to enjoy these things or putting up with them.