An obvious first step is removing downvotes so you can't completely obliterate someone who crosses sides to try to have a conversation, but after that, what else would help?
In my mind, some kind of code of conduct would help further those conversations, because it doesn't prevent people from expressing their opinions, it just makes them express them civilly. And if they express an opposing view without being overly antagonistic, then hopefully the other side wouldn't start insult slinging, and if they do, then that's what the COC would be there for.
I think there's a difference between having a "wrong" or "offensive" opinion, and expressing it in an offensive way. Do you think there's a way to achieve that balance, so that people can feel comfortable to express their opinions on either side, regardless of right or wrong, without it devolving into mudslinging and pure animosity on both sides? How do we accomplish that?