Have you ever stopped being friends with someone over differences in political views? Are there any issues that are so important to you that you cannot be friends with someone who holds a contrary opinion?
To which I must add one of my favorite RAH quotes: Always try to understand your enemy. It may leave room for him to become your friend. Or allow you to kill him without hate.
As for whether there are any issues that are so important to me that I cannot be friends if they hold a contrary opinion? A few. If someone tells me that he thinks there was no Holocaust and the Elders of Zion run the world, I'm rather unlikely to be friends.