Start by making a list of all the things they agree on. Then they could read them to each other. 

I liked it as soon as the words hit the air. I want to implement it and can hardly wait for a conflict to rear its snapping head. 

Then I realized there are already a fleet of impasses that have taken up residence inside my head. I disagree with this person about how they vote, and that person about how they hold marriage. But I can hop over the dispute and get to the juicy part, the vision they have for a healthy economy, or relationships where kindness matters more than income.

Jesus did this a time or two. The Samaritan woman was shocked that He could ignore her ethnicity long enough to speak to her much less offer living water. The woman taken in adultery was probably relieved that He could glimpse her humanity around the bulging evidence of her trespass. Christ did not agree with the politics of the Centurian whose daughter lay dying, or Nicodemus who came to him at night. Yet it did not seem like too big a leap of faith to start instead with what they agreed on, namely that twelve year old daughters should live and men should be born again. 

The next time John and I hit an unsolvable problem I will bring out a list of things we both love. In fact, there will be enough that I better start writing now.