State Department officials are afraid that if the high-profile U.S. intervention in the Persian Gulf is an embarrassing failure, it could encourage an Iranian-style tide of radical Moslem violence to sweep over Islam and even engulf non-Moslem neighbors.

Many Arab nationalists regard religious fundamentalism as the only force capable of breaking Western domination of Moslem nations. But these nationalists are far from confident that they could control a fundamentalist whirlwind once it was unleashed.

According to U.S. intelligence analysts, the dream of the nationalists is a union of the rich Arab oil states. This would provide the wealth, population base and military muscle capable of whipping Israel once and for all, and avenging the repeated humiliations the tiny Jewish state has inflicted on its Arab neighbors in the past 39 years.

Such a united Arab world would, of course, be a serious threat to American interests, not only because it would challenge Israel, a staunch U.S. ally, but because it would also, by definition, be an anti-Western coalition.

It is to discourage this neo-Nasserite dream of Arab union that the United States sends such huge amounts of aid to Egypt -- which has no oil, but has always been counted on to supply the Arabs' cannon fodder in their wars with Israel. But Egypt is one of the countries most vulnerable to Moslem militants. Thousands of religious extremists continue to prepare for the fundamentalist uprising they hoped would be sparked by the 1981 assassination of President Anwar Sadat.

Sadat's assassins were fundamentalists in the military, and President Hosni Mubarak has deployed a large portion of his intelligence agents to infiltrate the extremists in the six years since the assassination. The most violent Islamic elements in Egypt are home-grown. They are more worrisome than groups that are formed, fomented or financed by outside agitators in the pay of Egypt's enemies -- Libya, Syria and Iran. One native organization, which has survived repeated crackdowns, is the Moslem Brotherhood, which now has representatives in the Egyptian parliament.

Because of its moribund economy, Egypt is especially fertile territory for the Moslem fundamentalists' revolutionary propaganda. And the exploding Egyptian population -- 51 million and growing by a million every nine months -- makes nonviolent solutions even harder to effect.

Beset by its own problems, and dependent on U.S. aid, Egypt has pretty much ignored the U.S. initiative in the Persian Gulf. The reaction of the Gulf states, however, has been interestingly mixed, to put it mildly.

Bahrain, for example, has provided anchorage for U.S. warships and an airfield for dozens of transports that began a huge military airlift last June.

Kuwait, after asking for U.S. help, is considering a secret Reagan administration request that it at least ante up free fuel for the U.S. escort ships.

Oman is a staunch American ally, secretly providing military, logistical and intelligence support to the Western policing effort in the Gulf. Our sources report no signs that Oman is having trouble with internal fundamentalist dissent, but they were uncomfortably surprised by the congenial visit Iranian foreign minister Ali Akhbar Velayati paid last month to Oman.

Saudi Arabia's support has been about as strong as the United States expected from a regime that is still nervous about the recent Iranian uprising in Mecca. The Saudis have agreed in principle to allow AWACS surveillance planes to be moved to the mouth of the Gulf, and to permit U.S. fighters to land in emergencies.

The United Arab Emirates have been squabbling among themselves, but have been united in their resistance to the U.S. request for overflight privileges -- which would cut hundreds of miles from the distances our carrier planes must travel to the top of the Gulf.

Outside the immediate Persian Gulf area, the world's Moslems are watching and waiting to see what happens. From Afghanistan to Zaire, from Senegal to the Philippines, leaders of countries with predominantly Moslem populations or significant Moslem minorities are anxious to see how the Westerners stand up to the Iranian fundamentalists.