We've already mentioned the fact that two people cannot be exactly the same and that if they were, it would pretty much render the relationship pointless based on the fact that you'll never learn or grow from the experience of being with them.
Having said all that, it makes things extremely difficult if your basic values don't align. That means things like family values, your thoughts on raising (or even whether or not you want to have) children, even religion and politics.
We aren't saying that people from different religions (and of course, race, etc) can't have a very successful relationship, they've just got to be okay with the other and not a deal-breaker. It's a very good idea to get all these things on the table before they can potentially be an issue, because in a healthy relationship, these things all align and add to the greatness of the partnership.