To me, yes, to an extent. Political beliefs show your priorities and what you value, what you consider important. If my partner and I had conflicting political beliefs, it's likely that our outlook on things may be too different.
It matters, but not like your poll suggests. Not everyone has an issue of them voting for another party, but some of their beliefs can be deal breakers. Such as someone that wants a gun in the house to feel safe, and a person that is afraid of having a gun in their house.
Really depends on how far we differ. If she is an idealogue one way or another, that may be a problem. I'm fairly moderate, so someone that is extreme on one side or the other might be painful to deal with.
Yup. I cannot possibly deal with a right-wing crazy. If they were a moderate conservative, then yes. Anything from that to the ultra left where I am at, I can accept. But not far-right antics, impossible.