When I was younger, I would have said very important. But now I just think it's somewhat important. The more I see and hear in the world of politics, the more I realize that the different parties/viewpoints typically all want a better country/community/etc. (And I mean this more on the individual level because obviously on the national stage this is not necessarily true.) What differs is how they go about it. So, now I would say what matters more is a partner's moral character. How do you treat others, particularly people in need, animals, children.
I recently realized just how important this was during the Trayvon Martin trial. After the verdict, he and I were both devastated, stayed up late a couple nights just talking about the case and racism, etc. I can't imagine me almost in tears and dh being like Zimmerman was in the right . We disagree on a few things here and there but generally have the same fundamental political views.