How would you react/how have you reacted before to dating someone who ended up having different political views? Not even entirely but just disagreed with you on something?
I've ruined relationships because of this... I'll be stubborn and it makes sense to me at the time to be mad at the person, but until everything's over then I realize "shit... I forget I once believed differently than I do now... was it worth it?"
if you liked them before the dispute, chances are its not a huge difference in worldviews. However, you can still have the discussion as long as they are the kind of person who can handle debate. Otherwise its really just your own judgement call on if its worth the relationship and if you dont think they will change views.
It really shouldn't matter enough to ruin a relationship. You judge people by their actions, not their opinions, you'll find there are a lot of perfectly good people out there whose beliefs are very different from yours. And as you mentioned before, beliefs can change, a person's general nature and values and attitudes towards the relationship are much more important than what they have to say about today's current events.
Though these issues are weighty, you have to admit that most of our individual contributions are not. You're basically ruining a relationship over one individual vote. That's like dumping someone just because they really love Coldplay and you think Coldplay sucks. You might be able to convince yourself that you were right about Coldplay, but you're still alone