At the Vatican, Ronald Reagan meets a fellow actor who will be the stiffest competition -- and the greatest inspiration -- of his European trip.

The president and the pope, John Paul II, are both old-fashioned men who expound creeds much of the world finds outworn. They both have evidence that people who find their views unworkable or impossible nonetheless entirely approve of them as human beings.

Another thing they have in common is their belief that they can personally beguile vast numbers of people, and a faith in themselves that armors them in confrontation with hostile opinion. Both have exceptional gifts of projection, timing and delivery. The pontiff gave a performance in his tour of Britain that suggests that his gifts border on the supernatural.

The president wants to win over Europe, to convince the continent that he is a peaceable man. The pope's conquest of the English seemed to be as definitive as the Roman invasion of Caesar's time. He has set an example to Reagan of how tact, flair and charm can melt distrust and disdain.

The auguries for the first papal visit were so unpromising that the pope considered cancellation. Many stories about the commercial exploitation of the visit seemed destined to raise British hackles, which have never been entirely level since the time of Henry VIII. More immediately, the bitter fighting in the Falkland Islands was reaching a climax and the British press, not to mention the British people, was in the grip of a war fever that threatened to burn up the Thames. John Paul's announcement that he would balance the visit with a trip to Argentina did not increase the prospects of welcome. Vast demonstrations were threatened under the leadership of virulent anti-Catholics of the stripe of Ian Paisley of Belfast, who regularly refers to the institution which John Paul II leads as "the Scarlet Whore of Rome."

The pope decided to go and the strange thing was that the first papal visit to this Protestant country had about it the flavor of a homecoming. The British people seemed to need something they didn't even know they wanted. The television coverage was stunning: the pope in his white robes, kneeling in prayer by the side of the archbishop of Canterbury in Canterbury Cathedral; meeting with Scottish religious leaders in Glasgow, under a portrait of John Knox; holding a crowd in the palm of his hand in Cardiff, in the heart of Welsh Methodism.

Probably his greatest stroke was to venture a few words in Welsh, a language so difficult the Welsh can scarcely speak it.

By the time of his last appearance, it was all over.

"As I go away," he began, and the crowd roared, "No, no." He paused and fell back, then eyed them and said, with laughter in his voice, "As I go away," and there was another tumult of protest and laughter.

The demonstrations were of no consequence. The pope's sermons to his own flock repeating his strictures against contraceptives, divorce and abortion were received without comment. His plea for prayers for all who were suffering and dying in the South Atlantic was met with cheers.

He showed Ronald Reagan how it can be done.

Like Ronald Reagan, he can look at the numbers and see that in the world's esteem he fares better than his cause. The Catholic Church is in decline in almost every country except his native Poland. According to The New York Times, the shortage of priests in the United States is about to reach "crisis proportions." The number of seminarians has been cut in half. In Italy, despite the pope's vehement opposition, the citizens of an overwhelmingly Catholic country voted 2 to 1 in favor of retaining a law permitting abortion.

The Roman Catholic clergy has moved steadily to the left since Vatican II. In many countries, particularly Latin America, priests have been in the vanguard of protest and reform. The pope speaks for social justice and human rights, but is adamantly against clerical involvement in politics. Opposition to Reagan policies in El Salvador has been led by churchmen; the pope is said to be more receptive to the anticommunist line pushed by the White House.

Where he and the new breed are in entire unity is on the subject of nuclear war. Archbishop James V. Hickey of Washington is the latest prelate to speak out on what he calls, to the distress of Reagan, "a moral issue." The archbishop favors a nuclear freeze. The pope sent a delegation to call on the president last December to express his concern about "the breathtaking spiral in armaments."

The reviews of the visit of the self-proclaimed "herald of peace" were rapturous. Said the archbishop of Canterbury, "he has changed the map of Christian unity."

That is a hard act for Ronald Reagan to follow. But at least he knows that it is possible to win hearts -- if not minds -- and have a cosmic smash on your hands if you play it right.