Historic Mideast crosscurrents

The momentous crosscurrents sweeping the Middle East could bring radical changes in the political map of the region.

* Israel, for all its devastating military superiority, has overreached itself and is in danger of becoming trapped in the quicksands of Lebanon.

* The Palestine Liberation Organization (PLO) is having some success in the very risky business of trying to turn military defeat at Israeli hands into at least a qualified political victory. It has the example of the late President Nasser, who managed just that after the second Arab-Israel war of 1956.

* The United States is closer than ever before to dealing with the PLO - and to being recognized even by the more radical Arab governments as the only superpower which can effectively do anything to help the Arabs in this dangerous moment of crisis.

* This recognition has been reinforced by Iran's military thrust into Iraq July 13, putting the Arab Middle East on the defensive on both its flanks, with no clear Arab rallying point to meet the simultaneous threats from Israel and Iran.

* The replacement of Alexander Haig by George Shultz has underlined the gradual evolution of US policy toward the Middle East. At his confirmation hearing Mr. Shultz commented:

''The legitimate needs and problems of the Palestinian people must be addressed and resolved - urgently and in all their dimensions . . . . For (negotiations) to succeed, representatives of the Palestinians themselves must participate in the . . . process.''

Mr. Shultz balanced this by describing Israel as ''our closest friend in the Middle East.'' He added: ''(Nobody) should dispute the depth and durability of America's commitment to the security of Israel or our readiness to assure that Israel has the necessary means to defend herself.''

Israeli officials point to this part of Mr. Shultz's statement - and to opinion polls in the US indicating continued majority support for Israel among the American public. But Israelis cannot ignore either Mr. Shultz's forthright reference to the Palestinians or to the mounting wave of public criticism in the US for what is widely perceived as the ruthlessness of Israeli military operations in Lebanon.

There is a parallel paradox in the Arab and Palestinian reaction to the apparently shifting emphasis in US policy. Arab governments may recognize the significance of this shift and do their utmost to encourage it - as the Saudi and Syrian foreign ministers are likely to do if and when they meet President Reagan next week. But Arab and Palestinian public opinion, and even moderate Arab governments in public pronouncements, still castigate the US as Israel's patron which could have stopped the Israeli invasion of Lebanon, had it wanted to.

For Israel, the dilemma is that in the eyes of Prime Minister Menachem Begin's government, it stands to lose something whichever way it moves to try to break the military stalemate at the gates of west Beirut. The Israelis have, in fact, lost monopoly control - at least for the moment - of the power to make their own decisions regardless of what anybody else (and particularly the US) might say.

This fifth Arab-Israel war has already lasted longer than the second (1956), third (1967) and fourth (1973). This is despite the fact that the Israelis still have such overwhelming military superiority that in terms of raw power that they could bring hostilities quickly to an end in their own favor. But they could do that now only at a price.

That price would be the mounting Israeli casualties virtually certain if they tried to wipe out the PLO by storming besieged west Beirut, plus the international opprobrium which such a course would bring down on them.

The Israelis say they will not let the PLO drag them into a war of attrition. But there is the possibility of a war of attrition on their terms - hinted at by their occasional cutting off of west Beirut's water and power supplies, and the fierce artillery bombardment of the weekend of July 10-11. Those initiatives brought US government protests and another ceasefire.

There remains the evacuation plan for the PLO, with possible US participation to ensure safe-conduct elsewhere for the Palestinians. Admittedly, difficulties still beset that plan. But if put through with Israeli acquiescence, the Israelis know the Palestinians would have bought political (if not military) survival enabling them to participate in the kind of negotiations on their future outlined by incoming Secretary of State Shultz.

As for the Palestinians, even if the present situation in Beirut gets worse instead of better, they can find some satisfaction in their until now lonely struggle for survival.

They are still there in west Beirut, having born the brunt of Israel's military onslaught without help from any Arab government. This is the first Arab-Israel war in which they, and not an Arab government, are Israel's only foe on the battlefield. Israel is at bay - for the moment, at least. And both Israel and the US have been forced into taking them into account, even if still short of dealing directly with them across the negotiating table.