As Rep. John B. Anderson (RIII.) was about to leave Israel for Egypt the other day, he stood at the door of his chartered jet and executed a slow stage wave and a big smile in the direction of the tarmac below.

To the television cameras filming his departure, it looked as if the independent U.S. presidential candidate was acknowledging a farewell from Israelis who had come to Lod Airport to see him off. In reality, no Israelis had come, and nobody was down on the tarmac for Anderson to wave to except a few technicians, several policemen and a crew of traveling reporters, most of whom already were climbing into the plane through the back entrance.

The incident may have been extraordinary in American media campaigning. But there in Israel it seemed to symbolize what some Egyptians and Israelis found questionable about Anderson's new idea of exporting full-blown American presidential campaigning to the Middle East.

Wherever he went in Israel and Egypt, Anderson was operating on two levels, intended or not, just as he did in the contrived airport departure tableau.

On one level -- the one his media advisers worried about, and which some of them cited as the main reason for the trip -- Anderson was posing for U.S. television against the scenery of high diplomacy in the Middle East. At another, however, he was mixing his campaign into the serious business of trying to keep the Palestinian autonomy negotiations between Egypt and Israel alive and, ultimately, to prevent another Arab-Israeli war.

In Jerusalem, this produced cynical observations that the candidate was just politicking abroad for an exotic backdrop. It was hard for Israelis to resent it, because Anderson's positions on Middle East issues coincided nearly perfectly with those of Prime Minister Menachem Begin's government.

In Egypt, however, Foreign Ministry officials expressed private distress at what Anderson was saying. Reflecting their irritation, the Cairo press fulminated against Anderson's views and the fact that he should come to the Middle East to voice them for what editorial writers concluded were purely electroal reasons.

"An amateur should not bungle where experts have already burned their fingers. If getting into the White House is that important, Rep. Anderson would be wiser to confine himself to the hustings at home and not meddle in areas where he may cause greatharm to America's interests," the English-language Egyptian Mail wrote.

"Why is Anderson doing this?" asked one outraged Egyptian journalist angry that President Anwar Sadat received the candidate despite his Pro-Israeli declarations. "And why does Sadat see him? It is a disgrace."

Neither the Israeli cynicism nor the Egyptian anger cost the Anderson campaign very much -- the farewell looked good on television and the candidate succeeded in being photographed with Sadat. On a few other occasions, however, Anderson's aides and advance staff discovered that the mix of electioneering and Middle East diplomacy was not a happy one.

King Hussein of Jurdan and Mayor Elias Freij of Bethlehem, for example, both told Anderson they did not want to see him. The candidate's aides found good reasons why -- Hussein was hosting an Arab League foreign and economic ministers' conference that Freij also was attending. But Freij said out loud that he refused a request for a meeting because of Anderson's pro-Israeli campaign statements on Jerusalem and West Bank settlements. Observers were told that Hussein found himself too busy for the same reason.

In Cairo, reporters trying to pin Anderson down on his Jerusalem stand asked whether he believed Palestinian residents of East Jerusalem should vote in the elections that Israeli, American and Egyptian negotiators are trying to organize for the West Bank. This is and explosive issue in the talks because it revolves around question of Israeli sovereignty over the part of Jerusalem captured from Jordan in the 1967 war.

Anderson replied that he found merit in a suggestion that they vote with "absentee ballots," an idea he said he got from special U.S. Middle East negotiator Sol Linowitz back in Washington. Within minutes, his aides were urging correspondents to treat the declaration with "discretion," apparently fearing that Anderson could be accused of revealing a secret Linowitz stand in the talks.

Actually, according to diplomats familiar with the negotiations, the absentee ballot idea dates from last year when President Carter's campaign manager, Robert Strauss, was special Middle East envoy. It was never identified as a U.S. proposal, however, and the sources said it could embarrass Linowitz with the Egyptians and Israelis if it were made public as a U.S. suggestion favored by him.

Anderson said in the same conversation with U.S. correspondents that as a former Foreign Service officer he recognized the need for care in his statements on the delicate issures separating Israel from Egypt and both nations from the rest of the Arab world.

"I think there is a special obligation to some circumspection as to what you have to say," he declared.

Outsiders more accustomed to the Middle East than the election trail concluded, however, that an American presidential campaign -- even a circumspect one -- is difficult to export to an area where diplomats and their governments are still arguing over the campaign issues in an effort to prevent them from becoming battle cries again.