IN MOST Arab countries, the most popular public personality isn't Yasser Arafat. It is Muhammad Ali. From Morocco to Kuwait, Ali is revered almost as a hometown hero, and black Americans are considered brothers in Islam.

Meanwhile, in Chicago, in Harlem, all across America, many black Americans have turned to Islam and pray toward Mecca. Just as millions of Arabs consider black Americans exempt from their denunciation of American "imperialism" and support for Israel, so, for millions of black Americans, Moslem and Christian alike, Arabs are "blood brothers" -- sharing similar geographical and cultural roots.

In recent years, as tensions have grown between black and Jewish Americans, from the Crown Heights section of Brooklyn to the Supreme Court chambers where the Bakke and Weber cases were argued, Afro-Americans have experienced growing sympathy for the Arabs, especially for Palestinans displaced by Israeli expansion.

But, until the furor over the forced resignation of U.N. Ambassador Andrew Young, the American black establishment has made no move that would threaten its traditional friendship with American Jews.

So many years after Elijah Muhammad first made Islam a powerful force in black America, and the Arabs began equating Zionism with racism, U.S. blacks still know very little, and seem to care even less, about the Arab cause. For their part, Arabs in America and the Mideast seem equally unaware that an organized black leadership and society even exists in America, aside from Muhammad Ali and Andrew Young.

The Arabs so far have failed to exploit an oppotunity to win over to their case a group of more than 25 million Americans who, until recently, overwhelmingly supported Israel, U.S. blacks -- at a time when mainstream America seems increasingly insensitive to their needs -- also have made little effort to enlist the Arabs' growing political and already immense financial resources for their cause.

While the Arab-American dialogue is more intense than ever before, benign neglect in relations between Arabs and Afro-Americans is the rule even in the most radical Arab states. Libya, for example, has recently been receiving a steady stream of American visitors, ranging from Billy Carter to Spiro T. Agnew. But U.S. blacks have played no significant role in this dialogue. Last fall, when more than 100 American educators, lawyers and media personalities visited Tripoli at the invitation of the Libyan government, only two were black.

The omission of an Afro-American component in the Mideast dialogue has been especially noticeable in comparison to the Arabs' diplomatic and political efforts in black Africa. Of the Arab League's 21 members, eight -- Algeria, Egypt, Libya, Mauritania, Morocco, Somalia, the Sudan and Tunisia -- are in Africa. Nearly 100 million of the Arab world's 145 million people live on the Africian continent.

Part of the reason Arabs expend so little effort making their case to black Americans is that, from Marxists to oil sheiks, Arabs believe their society has no race problem -- and they find it inconceivable that others could think it does.

King Khalid of Saudi Arabia, for example, seemed genuinely astonished at rumors he had barred all blacks from the eighth floor of the Cleveland hospital where he underwent heart surgery last year. Khalid told Andrew Young and Rep. Louis Stokes of Cleveland that the rumors "hurt very much."

"He said that in his own family, he had been raised by a black woman," Stokes told the Bilalian News, a Black Muslim newspaper, after his meeting with the king, "and that all of his children had been raised by a black woman and that it would never occur to his family to discriminate."

The Saudi leader apparently was unaware how often American blacks hear similar statements from Southern whites about their black "mammies." Similarly, Arabs find it hard to believe that Afro-Americans worry about the Arab role in the slave trade, or take seriously charges by some American blacks, such as Eldridge Cleaver, that they have suffered racial discrimination in Arab countries.

Even the richest Arab oil countries also have neglected investment and philanthropic opportunities that might benefit both black Americans and themselves. While Arab governments have endowed Arab studies departments at two prestigious U.S. universities, and made major donations to the Cleveland hospital where King Khalid underwent surgery, none of the more than 50 U.S. colleges, nor the dozen or more hospitals, founded by American blacks have been beneficiaries of Arab support.

Meanwhile, supporters of Israel continue intensive efforts to maintain the support of Afro-Americans, including Black Muslims, in spite of tensions between the black and Jewish communities.

No Arab group makes any special effort to reach the black media. But the American Jewish Congress funds and staffs a special office, the Black Media Task Force, which systematically presents the Israeli position to hundreds of black publications and journalists each week.

While no Arab leader has ever spoken out in specific terms of civil rights issues like the Wilmington 10, Jewish Americans continue to provide major, if diminished, support for black causes.

No Arab-supported organization seeks to mobilize black American public opinion on the Mideast conflict. But union leader Bayard Rustin's Black American Support Israel Committee (BASIC) is so active that its membership includes most prominent black civic, professional and government officials, as well as black sports and entertainment figures from all over the country.

There are also other factors. "Zionism is imperialism," the fiery poet Amiri Baraka, a black nationalist turned Marxist, told me in an interview last fall. But even he concedes that it is "sobering for blacks when they come up against the class distinctions that exist, despite Islam, in the Arab world."

The middle-class black," adds an educational consultant here, "tends to fear Arabs because of the fear of being torn between the Arab position and the Jewish position."

One reason for such fear is that the Israel lobby does not hesitate to use the stick as well as the carrot. Four years ago, pro-Israel groups raised a $50,000 war chest and sought out pro-Israeli black candidates to oppose Rep. Ronald V. Dellums after he voted against an Israeli-supported arms proposal. Dellums overcame the challenge, but Archie Hargrave, former president of Shaw University in Raleigh, N.C., was less fortunate.

In early 1977, the black educator visited several Arab countries on a goodwill mission sponsored by the Arab League. Hargrave also attracted Arab and Iranian students to his financially pressed institution and hired a handful of American instructors of Arab descent. After his return from the Mideast, Shaw's trustees forced Hargrave from office. While the university had many serious problems under Hargrave's leadership, his supporters say it was his experiment in building bridges to the Arabs that sealed his doom.

The result is that while black leaders such as Maryland's Rep. Parren J. Mitchell occassionally point out "similarities between ourselves and the Palestinians as displaced people away from their homeland," almost all black leaders know that Arab rehetoric is no subsitute for the votes and financial support that good relations with pro-Israel groups can provide.

No black congressman has ever visited any of the Arab counties, though almost all have toured Israel several times. And despite current tensions, black leaders continue to reaffirm their desire to maintain Jewish-black dialogue.

Black Muslim Chief Imam Wallace Deen Muhammad, for example, has initiated an unprecedented exchange of visits with Washington Rabbi Joshua Haberman, with each preaching to the other's congregation. Imam Muhammad also declined an invitation to visit Libya, even though it was the Libyan government that six years ago lent his late father, Elijah Muhammad, $3 million to purchase the sect's first mosque in Chicago. Meanwhile, the most influential black publications, including Harlem's pretigious Amsterdam News, continue to call for conciliation and coalition between blacks and Jews.

The absence of effective black-Arab relations on any level contrasts sharply with the growing influence Afro-Americans have on U.S. policy south of the Sahara, and the support African officials now give U.S. blacks.

The Congressional Black Caucus frequently meets with high administration officials to propose policy toward Rhodesia, Namibia and South Africa, and Andrew Young, before the dispute that ended in his resignation, had emerged as the most important policy-maker in that area.

African heads of state also have expressed their concern to U.S. officals over the Wilmington 10, and other violations of human rights in the United States.

The old black-Jewish alliance in America may be in greater trouble than ever before, but Arabs probably will get only peripheral and ineffective support from U.S. blacks so long as their denunciations of Zionist "racism" are not matched by at least expressions of concern for those struggling against racism here. And black Americans will have little success in winning either Arab friendship or contracts until they, too, start treating the Arab connection as something more than an exercise in rhetoric.