Listen to why something matters to them, rather than to the details of the something.
As you listen, set aside, as much as you can, whatever the specific policy or vote or technical issue is about. And instead listen to why this opinion matters to the other person so much.
Why are they so passionate? What is under the surface? Ask questions. Listen much more than you talk. Understanding their perspective may not bring agreement, but it can bring empathy, even as you disagree. And that ability to understand what is in the other’s heart is crucial for the long-term relationship.