For a Christian, a top maxim in their value hierarchy would be rooted in Jesus' famous commandment: "Love the Lord your God with all your heart, soul, and mind." Now, if you're an atheist, this might be nonsense to you. You might not believe that Jesus was resurrected or that God even exists. To you, these are fundamentally irrational statements ("pigs can fly," etc.). Under your system, if you were an atheist and your opposition was a Christian, you could never possibly build a coalition because there's a disagreement at the top of the value hierarchy.

But this seems wrong because people of different creeds and value systems do stuff together all the time. Or am I misunderstanding your point? What I understand @Brendinooo to be saying is: "we may not share the same moral framework (or value hierarchy, using your term), but we do agree on X, so let's do X."