I have a few friends on the other side of the political fence and certainly on the other side of monarchy/republican fence.... I've found it's always best to focus on what unites us as friends and end any disagreement on that note. It's a tough ask sometimes because I am obviously 100% right on every issue even when I've changed my mind ;o) - but usually we can come to some place of common human understanding.
Not many people have a nihilistic view that wants to make the world a less pleasant place - they just have a different concept of pleasant.