I think one important distinction to hold is between the values themselves and HOW those values get expressed, i.e. behaviorally. Because getting behavior-based alignment tends to work better.
So, we can all agree to "treat each other fairly." But what happens when you think I treated you fairly and don't think I did? Now the conflict SEEMS to be about the value of fairness, but it's really not. Which makes it hard to update our agreement about what we expect.
It's just about different interpretations or strategies to express that value. Non-violent communication does a great job of explaining the distinction between a human "need," like safety, respect, love, and "a strategy," which is what we use to meet that need.
For example, I need to feel "valuable," but my co-workers aren't giving me the kind of positive feedback I expect. So, by reflecting, I realize that my strategy of passively just waiting around for positive feedback isn't really working. So, recognizing I need a new strategy (one that I have more control over), I decide to solicit positive feedback rather than just wait for it (e.g. "Hey everyone, I could really use a boost and was wondering if you would be willing to share anything I've done recently that's made a positive impact on you or your work...). That's the difference between a "need"/"value" and a "strategy"/"behavior."
Deep down, our needs (i.e. values) are never really in conflict, because we all need all of them. What comes into conflict are our strategies. And failing to make the distinction between the need itself and the strategy to meet the need creates all sorts of pain and confusion.
That's why behavioral agreements tend to work better, BUT coming up with new strategies or agreements then requires knowledge of the values or needs beneath them. So, values-work is still needed, just don't stop there.