Is it ever appropriate for a diplomat to express disagreement with his or her country’s leader?

Yes and no.

As a recent example, the U.S. Ambassador to Myanmar (formerly Burma), Scot Marciel, refers to the persecuted Muslim minority as the "Rohingya," despite requests from the Burmese government to do otherwise. But as the genocide has escalated, most diplomats directly stationed in Yangon have kept quiet, trying to preserve their influence with the government. (Still, outsiders from President Macron of France to Pope Francis have been critical.)

As an example from the past, the U.S. Ambassador to Nazi Germany, William Dodd, was told by FDR not to protest officially the persecution of the Jewish people. Dodd eventually resigned in what he thought was an impossible job, that is, maintaining diplomatic ties while staying true to principle (he also felt that the Roosevelt administration did not understand the threat of Nazi Germany, and he could do little to change that).

Diplomats walk a very fine line. Their jobs entail advocating for their own country's positions abroad while being respectful of the ways in other countries. Looking back, diplomats are often too cautious and unwilling to forcefully disagree with what is patently wrong. Would it be appropriate to disagree more? Maybe yes. But how would you feel, for instance, as the president, listening to a foreign ambassador tell you how to run your own country? It's a tough situation to say the least!