Secretary of State George Shultz' extraordinary outburst against "churchmen who want to see Soviet influence in El Salvador improved" has provided another chapter in the continuing saga of the irascibilization of the administration's Mr. Calm.

Imperturbability used to be Shultz' trademark, that and measured, thoughtful expression. But in China, he barked at a bunch of businessmen who complained of U.S. trade policy. Then, undiplomatically, he gloated over Qaddafi, "He is back in his box." More recently, he bristled and growled at House members inquiring about the possibility of negotiation in El Salvador. His brusque "No dice" rejoinder occasioned something nobody expected to hear in Washington -- a comparison with Alexander Haig -- which Shultz shirtily welcomed.

But this week's frontal attack on Catholic clerics advocating dialogue -- they conspicuously include the Pope -- is of a different order. It cannot be laid to travel strain, or the twin imperatives to be tough and a teamplayer in the Reagan adminstration.

John Paul II, whose current visit to Central America is considered by the administration as a dreadful threat to its already threatened plans for increased military aid to El Salvador, is a world figure. He has an enormous constituency important to any American politician. As a Pole, John Paul may not feel he has to be instructed in the communist menace. Nor may he appreciate being thought naive -- Shultz said in his testimony that people who do not say that their objective is communist takeover but nonetheless advocate policies which are bound to result in that effect are helping to bring it about.

Shultz was, of course reflecting White House panic over El Salvador. He was also echoing its outrage and frustration at the Catholic Church's refusal to see the war as stand against the Soviets and its satellites.

At the Senate Appropriations Committee hearing where Shultz took on the church, Sen. Patrick Leahy (D-Vt.) bore down on him about the Catholic bishops' repeated calls for "dialogue." the diplomatic term for negotiation. Leahy read to him the famous passage from a pastoral letter in which John Paul described the conflict as "a war placing on one side those who consider armed battle a necessary instrument for obtaining a new social order, and on the other side, those resorting to the principles of national security to legitimize brutal repression."

Shultz initially responded civilly that he was sure "that the motivations of people in the church, as all of us, are to establish peace." He went on to give the party line about the rebels who want "to shoot their way into the government."

But it was obvious that Leahy's provocations were rumbling around in his mind thereafter, and, minutes later, in response to a question from Sen. Arlen Specter (R-Pa.) about the plight of Soviet Jewry, Shultz exploded.

"It is a subject we bring up every time we meet with somebody from the Soviet Union and I suppose it is a subject that might be asked the churchmen who want to see Soviet influence in El Salvador improved."

Leahy thereupon asked Shultz to provide him with a list of these subversives in Roman collars.

Now the short fuse of George Shultz is a major topic in Washington. Speculation runs that he is called upon to do too much by the administration. That the burdened secretary, who has the whole world in his hands, is asked to sit in on matters like budget and international monetary concerns. It is not forgotten that the first public event he attended three days after he was confirmed by a joyful Senate last July was a rally for the balanced- budget constitutional amendment, as if State were just one of his duties.

But, according to some sympathetic observers, Shultz is suffering from more than stress and fatigue. Their grave theory holds that the secretary, in his heart, agrees with the Pope that a political solution is the way out in El Salvador.

Shultz was, after all, secretary of labor. His instinct and experience would make him pro- negotiation. The speculation is that the short- lived "two-track plan" for promoting talks while continuing military aid was his way of going about the problem in a non-violent way. The plan was floated by his subordinate, Thomas Enders, assistant secretary for inter- American affairs. It was promptly drowned in White House denials.

Shultz, it is thought, lost the argument against the hard-liners, namely National Security Adviser William P. Clark and U. N. Ambassador Jeane Kirkpatrick. He berated the subversives in Roman collars because he was anguished more than angry.

"What George Shultz did the other day," said somebody who is on his side, "is to show what bad policy can do to a good man."