The influence of Nazism on various pan-Arab nationalist groups is highly contentious and politicized. There is no shortage of popular commentators that build on linkages between the Arab nationalists in the 1930s and early 1940s and the Third Reich. In some cases, this builds up to a charge that Arab nationalism was a species of fascism and shares many of its precepts of global domination. Conversely, there are commentators that deny the importance of Nazism to the political activism of the thirties and rejects any political connection between fascism and Arab nationalism. Neither approach presents an accurate picture of this period and its complexities.

In terms of form and some content, the Arab political movements of the 1930s did take some inspiration from the European political scene. Although the NSDAP and Germany were one model to emulate, it was Mussolini, not Hitler, that elicited more interest. With its corporatist model and more intellectually rigorous approach to politics, Italian fascism presented a much more relatable phenomena than Hitler's very German-centric brand of politics. Many Arab nationalist movements within the 1930s looked to Italian fascism as an organizational model, especially its paramilitary formations and leadership cult. The corporatist model had also seemingly worked in Turkey, which added to the attraction of the Italian paradigm. Arab political groups were far from alone in emulating the fascist model. Some Zionist groups and many European nationalist movements such as O'Duffy's Blue Shirts took cues from il Duce in the form of organized paramilitarism and a more militant form of nationalism. Fascism's promise of national regeneration and strength had currency in the context of the demi-colonialism of the Mandate period as it provided both an organizational model for resistance as well as a post-colonial model for government.

One charge often leveled against Arab political movements by the likes of Sam Harris was that they imbibed Nazi antisemitism and this has metastasized in the current invective against Israel. The Mufti of Jerusalem, Haj Amin al-Husseini, was an avowed Nazi sympathizer and active supporter of the Third Reich's actions against the Jews. He did conduct propaganda broadcasts during the war to stir up Palestinians against Zionists and the British occupation. Jeffrey Herf has made much of these broadcasts in his monograph Nazi Propaganda for the Arab World, in which he lays the origin point of Arab antisemitism in these wartime broadcasts. But Herf never really proves that this propaganda found a wide receptive audience within the Arab world. Very few Arabs owned shortwave radios and there is no real evidence one way or the other that they listened to the Third Reich's propaganda. Herf asserts that Sayyid Qutb might have been influenced by these broadcasts, but Qutb's antisemitic essays only appeared in 1951 after the first Arab-Israeli War. Joel Beinin's review of Nazi Propaganda for the Arab World sums up this problematic method rather well and is worth quoting at length:

Herf speaks ominously about “the merging of National Socialist with radical Islamist anti-Semitism and its diffusion to the Middle East” (p. 11). There is no easy way to determine how many Arabs listened to Nazi propaganda broadcasts or their reactions to the message. So, Herf resorts to speculative formulations like, “It is plausible that during World War II, Sayyid Qutb listened to Nazi broadcasts and traveled in the pro-Axis intellectual milieu of the radical Islamists in and around Al Azhar University” (p. 259). We don't know what radio broadcasts Qutb may have listened to. However, because Adnan Musallam's biography of Sayyid Qutb is in his bibliography, Herf should know that it was not until his visit to the United States from 1948 to 1950 that Qutb repudiated Western liberalism and began writing about Islamic themes (Adnan A. Musallam, From Secularism to Jihad: Sayyid Qutb and the Foundations of Radical Islamism [Westport, Conn.: Praeger Publishers, 2005]). Qutb did not join the Muslim Brothers until the early 1950s. His anti-Semitic essay “Maʿrakatuna maʿa al-Yahud” (Our Battle with the Jews) appeared in 1951, after the first Arab–Israeli War. This chronology, although it in no way excuses it, establishes a very different context for Qutb's anti-Semitism. The case for a link between Nazi propaganda and Sayyid Qutb's views about Jews rests on conjecture and innuendo, as does much of what Herf offers when he ventures beyond the terrain of Germany.

Far more persuasive than Herf is the work of Israel Gershoni and James Jankowski who assert that wartime fascist propaganda fell on deaf ears within most of the Arab world. Most Arab public intellectuals saw fascism as a more malignant form of Western colonialism and saw German propaganda as self-serving. Arab political groups may have taken cues from fascism in terms of political self-styling and aesthetics, but this did not translate into sympathy for the fascist cause during the war. Meir Litvak and Esther Webman have backed up this assertion by a deep analysis of Egyptian newspapers that reveals that between 1945-46, they regularly and accurately reported on the Holocaust and expressed a degree of sympathy with the Jewish victims. The Arab-Israeli wars led to a sea-change in Egyptian papers and then is when Holocaust denial and minimization gained traction within the Arab public sphere.

Even al-Husseini's extremism and involvement with the SS needs a proper contextualization. The Germans never devoted much in the terms of resources or attention to the Arab cause, and most of the conventional bureaucrats in the Italian and German foreign ministries favored other Arab leaders. After the failure of the Iraq revolt in 1941, al-Husseini ended in Europe and worked for the German propaganda machine. But in doing so, he had to compete with other anti-British Arab emigres and navigate the various factions within the German state apparatus. Al-Husseini's anti-Jewish sentiments put him in ideological resonance with the SS, but in light of other emigre competitors like Rashid Ali al-Gaylani, making an alliance with this particular power bloc had a certain political logic behind it. Al-Gaylani's more secular and pan-Arabist politics had found support both in the Italian and German foreign ministries and he was in many ways a more "current" leader against the British, having participated in the Iraqi revolt in 1941. Al-Husseini's main stand against the British had occurred a generation earlier in 1929. Making the most of his connections to Himmler was a way for al-Husseini to gain the paltry resources the Axis devoted to the Arab cause away from an emerging rival.

One of the problems with saying the Arabs "borrowed" elements from fascism is that it denies Arabs real agency in creating their own political movements. As the case of al-Husseini demonstrates, there was a political logic to the actions of some that cannot be simply ascribed to sympathy for fascism and its ideology. Conversely, denying the presence of any Arab engagement with European politics projects an insularity onto the Arab public sphere that borders on the farcical. Of course Arab public intellectuals and ideologues were aware of wider events in Europe and adjusted their movements accordingly. Writers like the Egyptian pan-Arabist Ahmad Hasan al-Zayyat could alternate between condemning Nazism's racial theories and extolling the virtues of Germany's economic regeneration under Hitler. There were elements of fascism that attracted Arabs in the interwar period, but also elements of its ideology many Arab nationalists found repellent.

Sources

Gershoni, I., and James P. Jankowski. Confronting Fascism in Egypt: Dictatorship Versus Democracy in the 1930s. Stanford, Calif: Stanford University Press, 2010.

Gershoni, Israel, editor. Arab Responses to Fascism and Nazism: Attraction and Repulsion Austin, TX : University of Texas Press, 2014.

Herf, Jeffrey. Nazi Propaganda for the Arab World. New Haven [Conn.]: Yale University Press, 2009.

Litvak, Meir, and Esther Webman. From Empathy to Denial: Arab Responses to the Holocaust. New York: Columbia University Press, 2009.

Nicosia, Francis R. Nazi Germany and the Arab World. Cambridge: Cambridge University Press, 2015.

This is a false equivalence. Arab Nationalism did not draw influences from Nazism (it predates Nazism by decades); rather, they both draw from European concepts of nationalism.

TL;DR: Arab Nationalism predates Nazism and relied on the modernisation of Arab nations and opposition to European imperialism. When the early 20th-century Arab Nationalists failed to free themselves from imperialism, their kids turned to Pan-Arabism (the idea of a unified Arab sphere) as a means of resistance. Pan-Arabism, which was opposed to imperialism, opposed the formation of Israel (a Jewish state relying on Jewish Nationalism aka Zionism) which they viewed as a product of European imperialism. As such, after being routed by the Israelis, Arab leaders claimed Israel as the main enemy of their resistance to imperialism. As such, anti-Semitism mixed with Pan-Arabism.

This is where you are confused. Though Pan-Arabism (at least elements of ) and Nazism share anti-Semitism, anti-Semitism is not exclusive to Nazism.

. . . .

The roots of Arab Nationalism (short-hand: AN) began with Muhammed Ali Pasha, who declared semi-independence from the Ottoman Empire in the 19th century. Though from Albania, he was given command over Egypt by Ottoman Authorities. He was to put down separatism amongst Egyptians. However, rather than that, he killed the most prominent aristocrats over dinner and began modernising Egypt: politically, economically, militarily, and socially. Though angering Ottoman officials, they gave him temporary approval to govern Egypt (& Sudan).

This is the beginning of the al-Nahda or Arab Rennaissance. Though the movement started in the late-19th century with Ali Pasha's descendants, he laid the foundation. His first major step was to send his civil servants and military commanders to France, Great Britain, and Italy. Through their European studies, he coopted these concepts and translated them for Egyptian society. He modernised the military through a massive restructuring from the former Ottoman theories revolving around a sort of feudalism to modern European theories as well as importing modern equipment from Europe - mostly rifles and artillery. That gives you an idea of where he was taking Egypt.

The policies of him and his descendants gave rise to the effendis (or middle-class Egyptians), who were about 10% of the population by the late-19th century. It was this product of the 19th century, which became the center of the Arab Nationalism movement. Having an educated middle-class means having a richer, more varied demands - urban centers, newspapers, schools, roads, factories, et cetera. This makes them the sociocultural pioneers in Egypt rather than the aristocracy. The same happened in Europe a few decades earlier when liberalism was on the rise. When you lose the sociocultural leadership of the aristocracy, new theories are formed. In Europe, it was nationalism. Attachment to a nation-state replaced loyalty to a king because the few turned into the many, in a sense.

As it migrated to the Middle East, Egyptian effendis began to draw from ancient Egypt as a form of national pride, similar to how Europeans drew from their long history within each nation-state as their pride. However, this is where AN and European Nationalism divides. Because of his and his family's policies, he became semi-independent from the Ottomans, which became a problem from both the Ottomans and the European imperial powers, who had deals with the Ottomans and not the Egyptians (they also wanted the land for the canal). As such, the Ottomans invaded Egypt and fought a war of independence. Though Egypt won strategically (they ended up independent from the Ottomans), their inability to fight off the Europeans meant they became a mandate under the British and the French, from which the British ended up with complete control.

Despite meaning greater access to European markets and education for the effendis, it was a massive strike to their pride as Egyptians. This is what lead to Arab Nationalism. Egyptian Nationalism migrated to other modernising areas, such as Lebanon, Syria, and Palestine, all of which ended up under European control either directly or indirectly. Because of their shared opposition to Europeans imperialism, academics and journalists from Egypt and Lebanon began pioneering Arab Nationalism, which resulted in Pan-Arabism in the mid-20th century.

There aren't any Nazi influences in Arab Nationalism, but I might see where you are getting confused. Pan-Arabism was a successor ideology to Arab Nationalism after young Arabs saw their parents' failures to combat European imperialism. They didn't abandon AN, but they understood that deals with the Europeans would not be honored and coercion/force must be used. This is what gave rise to the authoritarian socialist states in Iraq, Syria, and Egypt.

While the foundation was still opposition to Europeans imperialism, which is why the term "third-world" was coined due to Egypt's Nasser's leadership of the neutral states during the early Cold War, Israel became a throne in the Pan-Arabism's side. They viewed Israel as the last imperialist presence in the Middle East, meaning that it needed to be defeated for them to achieve complete victory over the European powers. Well, we all know history.

So here is where your false equivalency comes from: the concept of Israel is fundamentally Jewish - a Jewish homeland for an exiled, stateless people. Therefore, Israeli Nationalism is Jewish Nationalism, aka Zionism. As such, opposition to Zionism (aka Jewish Nationalism) became anti-semitic. To rally their people, Arab powers began utilizing the exile of Palestinians (al-Nakba) and their oppression under Israel as a unifying symbol. In rhetorical terms, the Palestinians became the same as all Arabs (figuratively, not literally as we can see by how they were treated). Israel was the oppressor and enemy of Palestinians; therefore, the enemy of Arabs. As such, Pan-Arabism became mired with anti-Semitism that wasn't mainstream only a decade before. Because of this, some Arab scholars began drawing from European anti-semitic propaganda from the 20s, such as The Protocols - a book from the early 20th century that tried to make the case that Jews and the "Elders of Zion" were trying to take over the world.