[The labels "liberal" and "conservative" ("traditional(-ist)" likewise) are of course inadequate, if not pernicious, but labels have their uses and we all know what these ones mean (more or less). It is with this caveat that they are used here.]
It's not exactly an amazing insight to say that in their disagreements (and even in sincere attempts at dialogue) liberal and conservative Christians are usually taking past each other.
It is not, however, so often noted that the problem is exacerbated, if not actually caused, by agreement about first principles, not disagreement.
Almost everyone (liberal or conservative)* would assent to the propositions that Christians should both be faithful to the Gospel and preach that Gospel anew in every age.
But the key question is: What does this mean in practice?
To the conservative, the liberal's concern for preaching the Gospel anew tips over into unfaithfulness.
To the liberal, the conservative's concern for faithfulness ends up killing the Gospel.
The conservative finds it hard to believe that her liberal brother really cares about faithfulness, but it's precisely because he does that the liberal gets mightily offended at the implication that he doesn't.
The liberal finds it hard to believe that his conservative sister really cares about bringing the Gospel to the present age in any useful way, but it's precisely because she does that the conservative gets mightily offended at the implication that she doesn't.
How far is too far? How far is not far enough?
* Naturally there are exceptions at the extremities, and there are, too, some people who for pragmatic reasons are suspicious of perfectly reasonable formulations like these.