There are a few things that changed there, but perhaps the biggest is the continuing collapse of the Soviet Union, and the diplomatic shifts that it wrought.
1975 was, perhaps, a peak in the Arab world's economic and political clout. The Soviet Union was a strong ally to much of the Arab world, despite some fraying starting to show. Egypt and Syria had bloodied Israel in the 1973 war, albeit being in a fairly bad position militarily at the end of the war. The oil embargo put in place by OPEC had demonstrated a serious ability to place economic pressures on the United States and the West.
The interests of the Arab world should already be clear with respect to Zionism and Israel. The Arab world was still adhering, at least publicly, to the position that Israel's existence would never be accepted, in line with the 1967 "three no's" at Khartoum (no peace with Israel, no negotiations with Israel, no recognition of Israel). That alone, in 1975, meant that at least 10 states were already pushing strongly for the resolution as a way to delegitimize Israel (Algeria, Bahrain, South Yemen, Egypt, Iraq, Jordan, Kuwait, Lebanon, Libya, Qatar, Saudi Arabia, Syria, Tunisia, United Arab Emirates, Yemen).
When you consider this, as well as the clout of the Soviet Union, it makes sense that the resolution was able to pass. The opposition of the West and parts of Asia was insufficient to stand against this type of concerted diplomatic effort. In fact, some have posited (like Gil Troy in "When Oom Became Shmoom", referring to an Israeli saying that became popular especially after this resolution, "Oom Shmoom", meaning essentially "the UN? Whatever, who cares") that the resolution was voted in by a smaller majority than expected, which may in part be due to the US stance and the fact that the very resolution impliedly violated the UN Charter's goal of respecting self-determination and seeking peace. As George H.W. Bush put it in 1991 when endorsing the repeal of the resolution, rejecting Zionism is to reject Israel's very existence, despite its status as a member in good standing at the UN. Challenging Israel's right to exist would be contrary, impliedly also, to the goal of seeking peace.
The Soviet Union's anti-Israel position, motivated in part by its alliance with the Arab states and in part by antisemitism, is well-documented. However, not a lot of folks are aware that the Soviets did their best to export antisemitism to other countries as well, especially out of the belief that Zionism was part of a global conspiracy heralded by capitalism.
The KGB and satellite spy agencies were deeply involved in this exporting of antisemitism to the developing world, including even to the Arab world. This is not to say that antisemitism began with the Soviets there; it had already been spreading by the 1800s in classical form. But I think there’s room to argue that Soviet exports of antisemitism strengthened and played off the fears of antisemitism that already existed in the Arab world and elsewhere for political gain. The campaign took on new fervor following the Israeli victory over Egypt, Jordan, and Syria in 1967, which embarrassed the Soviets who had supplied the Arab states with much of their weaponry.
The Soviet campaign was not just to paint Zionism as Jewish self-determination or Israel's existence and racist as a result. It wasn't just to oppose "nationalism" and thereby oppose Zionism as well. Instead, the Soviets painted Zionism as a "world threat". As Howard Sachar put it in A History of the Jews in the Modern World, the reason the Arab states lost was because of an "all-powerful international force" that was composed of "Jewish communities everywhere", not just Israel. The Kremlin now spoke of "the power of world Jewry", and "Zionists" were portrayed as "rich Jewish bourgeoisie", contrasted with the good Soviet communist. Zionism was seen as synonymous with global capitalism and excess, and the Soviets exported this ideology fervently, claiming that the United States was just a puppet of the Zionists, and telling the Muslim world that Israel and the US would try to turn the Muslim world into a Jewish territory.
This diplomatic onslaught slowly weakened as the Soviet Union did, and as Egypt made peace with Israel in 1979. The United States, which had fought against the resolution as racist from the moment it was proposed, experienced a resurgence in influence at the United Nations with the fall of the Soviet Union.
But the resolution was set up for repeal before the Soviet Union formally dissolved. In fact, the Soviets supported the revocation in 1991. It was a mere 10 days before the dissolution actually took place. This was a byproduct of the Soviet collapse, and reversal of many policy positions. As I said at the start, not many realize exactly how ingrained the Soviet Union was in the process of anti-Israel positions in international bodies throughout its existence. For a state that had ostensibly made antisemitism a crime, many of its policies were motivated by, or at least spread through, an industrial campaign of antisemitism spread that replaced the word "Jewish" with "Zionist". And so, as Soviet influence waned, so did the ability of this campaign to bear fruit. The effects of Soviet propaganda about Zionism would continue to bear fruit worldwide, but the resolution's revocation came at an opportune moment when the diplomatic stars aligned. Portrayals of Zionism as an "international force", and as a racist endeavor, would not end with the Soviet Union's collapse, however; they would only be delayed.
Disclaimer: I am not a professional historian and I do not have a background in Israeli/Palestinian politics. I will use reliable sources and avoid editorializing the facts. I'd also like to stress that nothing I write here should be read to imply a moral equivalence between Zionism and anti-Zionism. I hope the mods have mercy on me.
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Your question is loaded in two ways. First, it presumes that global opinion drove the UN General Assembly to condemn Zionism in resolution 3379. Second, it refers to an amorphous "global opinion," which risks simplifying the issue and ignoring the many different points of view on Israel, Palestine, and Zionism that existed in both 1975 and 1991.
But if we read your question charitably, we might word it like this: Why did the UN adopt a resolution calling Zionism "a form of racism and racial discrimination" in 1975 only to revoke it less than two decades later?
The UN adopted the Declaration on the Elimination of All Forms of Racial Discrimination in 1963. This human rights instrument flatly condemned discrimination on the basis of "race, colour, or ethnic origin." By this point, Israel had already been a member of the UN for around twenty years. But in the period between Israel's admittance to the UN and the adoption in 1975 of resolution 3379, several armed conflicts occurred: the Suez Crisis, the Six Day War, and the Yom Kippur War, to name a few. Tensions rose and kept rising between the Jewish inhabitants of Israel, the Muslim Palestinians who lived there, and the nearby established military powers.
Israel served as a focal point for the wider conflict and global rivalries of the Cold War. The United States and the Western Bloc largely supported Israel, while the Soviet Union and the Eastern Bloc largely opposed it. Of the seventy-two states that supported the resolution, a large proportion belonged to the Eastern Bloc; the thirty-five states against, however, consisted mostly of western nations aligned with the United States. A further thirty-two states abstained from the vote. But GR 3379 cannot be explained solely by the Cold War and the worldwide tug-of-war between American and Soviet interests. Why, then, did so many African states vote for the resolution? Why so many Latin American states?
For the African states, here's the short of it: apartheid. The resolution itself made three explicit references to South Africa's notorious system of racial segregation. First, it quoted a document composed that year at the World Conference of the International Women's Year that called for the elimination of "colonialism and neo-colonialism, foreign occupation, Zionism, apartheid and racial discrimination in all its forms"; second, it quoted a resolution adopted by the Organization of African Unity stating that "the racist regime in occupied Palestine and the racist regimes in Zimbabwe and South Africa have a common imperialist origin, forming a whole and having the same racist structure[.]" Finally, and most prominently, it referred to a prior GA resolution against the "unholy alliance between South African racism and Zionism." These paragraphs drew a direct connection between South African apartheid and Zionism and equated them as imperialist and racist ideas. In its article on the 1991 revocation of GR 3379, the Washington Post put it simply: "Many of the [states voting for GR 3379] were African countries that wanted the support of the others for U.N. moves against the apartheid system of racial separation in South Africa." In other words, the issue of Israel and Palestine had turned into such a political flashpoint that some African delegations thought that voting together would give them enough influence to sway the UN against apartheid. This explanation seems to glaze over the actual feelings African states had about Israel -- maybe someone with more insight into 1970s African politics can jump in here -- but it makes sense.
What about Latin America? The Cuban and Brazilian arguments during the debates for resolution 3379 -- which, by the way, is a fascinating read -- are telling. Cuba spent some time drawing a distinction between Zionism and Judaism, pointing to the rifts within the larger Jewish community about the establishment of the state of Israel and Zionism's continuation beyond that goal, and it went to great lengths to compare Israel with the colonialism that Cuba once fought against. Brazil made many of the same points: Zionism had run its course, and the connection between ethnicity and Israeli citizenship -- Cuba used the Law of Return to illustrate this argument -- is essentially a form of racial discrimination. But pay close attention to the arguments of the states that ultimately abstained, especially Kenya. Its delegation complained that no one had actually defined Zionism or clearly explained its connection to racial discrimination: "Indeed, apart from expressions of anger or sometimes insults . . . what has been going on [here] sheds little or no light at all on the subject [of Zionism]." This followed a decision by the General Assembly not to delay voting on the resolution pending a study into Zionism and its effects. Some of the states that ultimately abstained had voted for this delay. Mauritius lamented that many of the "small" nations at the UN had caved to the influence of the "larger" ones, probably referring to the U.S. and the USSR. It criticized the Western Bloc's hardline stance against the states in support of the resolution and chastised the other side for the same reasons.
So... what changed?
Ask yourself what else was happening in global politics in 1991 and you will have part of the answer. The Soviet Union was on its way out, rapidly opening itself to foreign influence and heading towards dissolution. The once-unified Eastern Bloc had deteriorated and no longer had the political capital to overcome regional politics and internal conflicts. In 1975, "in an effort to curry favor with the Arabs and embarrass the United States, Moscow took the lead in pushing through the statement on Zionism," as the New York Times put it; in 1991, that kind of collective effort -- and the USSR's international arm-wrestling match with the U.S. -- could no longer continue. This time, 111 nations voted for resolution 46/86, which would revoke GR 3379. Only twenty-five voted against it.
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