You'll be genuinely interested in this friend as well as the friendship itself, and you'll really want to support each other and share your lives and experiences. But some basic differences will keep driving a wedge between you. You'll disagree over and over on the same certain subjects, and while you might be able to smooth things over easily enough, you'll still have the nagging feeling that something's not quite right between you.
It's not that you won't genuinely like and respect each other, but you'll differ on so many subjects, big and small, that you'll have a hard time finding any common ground. Compromise and adjustment are going to be necessary to smooth the way in this friendship.