In the afterglow of the Venice summitry, it is nice to think of the fine show of solidarity. It helps you forget that the allies never got around to the hardest part of the problem of how to keep the Persian Gulf safe for the free flow of oil (at reasonable prices) to the gas tanks, homes and factories of the West.

Let us assume that the seven richest Western allies make good on their firm commitment to reduce considerably their reliance on oil by 1990, by shifting to other energy sources. That still leaves a decade of dangerously heavy dependence on Persian Gulf oil, and a substantial dependence thereafter.

And let us suppose that the Soviets do want to find a face-saving way out of Afghanistan; that they were chastened by the allies' united call for "complete withdrawal" of Soviet troops; that they would lend themselves to a concerted alied effort to negotiate some kind of meutral, non-aligned status for Afghanistan. That's assuming a lot.

But, never mind; even if Moscow's tentative, minuscule first troop "withdrawal" is to be interpreted as a sign that the Soviets are looking for a way out of their Afghanistan quagmire, it scarcely follows that they have lost interest in the Persian Gulf's oil treasure, either for their own use or merely for the sake of denying it to the West. In any case, the Russians aren't the only source of turmoil in the Persian Gulf.

So the part of the Persian Gulf problem that the allies didn't get around to in Venice would still be there without the Soviets in Aghanistan. The question is still going to be how to provide stability in a chronically unstable corner of the world that will continue to be crucial to the industrialized West (and the developing Third World, as well) for many years.

And the answers you get in this city from an assortment of British and other authorities on the Persian Gulf make an instant shambles of allied solidarity. Merely to mention the Carter Doctrine is to start an argument. Says one British diplomat: "There is a severe schism between the United States and the European view of how to provide for the security of the Persian Gulf."

The argument you get into over the Carter Doctrine is only partly with its prescription -- the establishment of military "installations," the pre-positioning of military supply ships and the creation of a rapid deployment force capable of instant intervention in support of friendly governments. The argument begins with the Carter diagnosis of some unspecified threat from "outside forces" -- a threat the president said would be "repelled by use of any means necessary, including military force."

It is not that the British and other allies see no threat. The London Times acknowledged the other day that "the alliance faces the most complex and alarming world crisis since the end of the Cold War."

But most British and European analysts discount the possibility of an attack by "outsiders," whether the Soviets or their surrogates -- South Yemen against Saudi Arabia, for example. Beyound that, no more than the late John L. Lewis believed you could "mine coal with bayonets" do they believe oil production could be ensured by American military intervention -- anywhere.

The main threat they see to the oil flow is internal upheaval.Thus, they fear that a big show of supportive American military force in the area is more likely to embarrass than strengthen local regimes -- and to weaken them against coups d'etat or internal subversion by outsiders.

Similarly, they see U.S. efforts to prod Saudi Arabia into high oil production and low prices as something that plays into the hand of potential opponents of the royal government by making it look subservient to its "american masters." They would have the Carter administration save Egypt's Anwar Sadat from himself by not accepting his every offer of bases and supply facilities.

The Europeans' sense of how to reinforce the Arab oil countries and stabilize the area is nowhere better demonstrated than in their celebrated "initiative" in the Arab-Israeli conflict -- at the risk of upsetting the Camp David process.

The authorities here and on the continent may have it all wrong. The point is that they have it quite differently from the Carter administration. And that, in itself, is a threat to Persian Gulf stability.