I do believe (but please correct me if I'm wrong) that Hitler outlined in Mein Kampf that he saw Japan (as well as good old blighty as can be seen in regards to the looming 1935 Anglo-German Naval Agreement) as a possible ally with regards to targeting international jewry.

This is what Hitler had to say about the British, the Japanese & his thoughts on making them both possible allies. Even though the following passage focuses mainly on Japan. This is from Mein Kampf:

It was not in the interests of Great Britain to have Germany annihilated, but primarily a Jewish interest. And to-day the destruction of Japan would serve British political interests less than it would serve the far-reaching intentions of those who are leading the movement that hopes to establish a Jewish world-empire.

The Germans, like the other user mentioned coined the term Ehrenarier ("Honorary Aryan"). You might think what? Why would Hitler give the Japanese who weren't blonde-haired or blue eyed a pardon? Well in the beginning of the Nazi's Ideology, it was simply "blonde-haired, blue-eyed". No if's or buts. But as time grew on being "Aryan" was more about blood, this can be seen in the issuing of the Ariernachweis ("Aryan Certificate") & Ahenpass ("Ancestor Passport") this was given on the grounds of having at least one aryan family member (this could go back to 1800 for normal civilians or 1750 for SS members)

Also in the progression of Nazi ideology, Was the "Honorary Aryan" & this fell into place for all Japanese civilians after the 1936 Nazi-Japanese, Anti-Comitern Pact. "Comitern" was the abbreviation of the "Communist International" organisation (set up by Lenin in 1919, it advocated world communism). The Japanese were given this status not because of their racial integrity above anything else.

This is what Hitler stated about this status in The Political Testament of Adolf Hitler which was a part of Hitler's Last Will & Testament:

Pride in one's own race – and that does not imply contempt for other races – is also a normal and healthy sentiment. I have never regarded the Chinese or the Japanese as being inferior to ourselves. They belong to ancient civilizations, and I admit freely that their past history is superior to our own. They have the right to be proud of their past, just as we have the right to be proud of the civilization to which we belong. Indeed, I believe the more steadfast the Chinese and the Japanese remain in their pride of race, the easier I shall find it to get on with them.

The Japanese were quiet shocked at the Anglo-German Naval agreement, someone who held this view that is worth noting is Isoroku Yamamoto. Yamamoto thought this agreement was a mere ruse to buy the Nazi's more time to match the British navy (sounds a bit like Jamais vu, don't you think?)

Hitler admired Japan from a young age, General Tomoyuki Yamashita had this to say on Hitler's weeaboo like nature:

I felt, that in the mind of Hitler there was much of spiritual matters, transcending material plans. When I met the Führer he said that since boyhood he had been attracted by Japan. He read carefully reports of Japan's victory over Russia when he was only 17 years old and was impressed by Japan's astonishing strength.

Even after all of the "happy families" type relationship between Japan & Germany, the Japanese foreign affairs minister had this to say:

I am the man responsible for the alliance with Hitler, but nowhere have I promised that we would carry out his anti-Semitic policies in Japan. This is not simply my personal opinion, it is the opinion of Japan, and I have no compunction about announcing it to the world.

I'm sorry that I can be of more help & go into more detail but that is the limit of my knowledge, but I hope that what I have discussed has been enlightening :)

Further Reading & Sources:

1. Mein Kampf, Chapter 13: German Alliance Policy After the War ~ Adolf Hitler

2. The Political Testament of Adolf Hitler, Note #5 ~ A. Hitler

3. Yamamoto: The Man Who Planned the Attack on Pearl Harbor ~ Edwin P. Hoyt

4. World: Is Hitler Running Japan? ~ TIME Magazine, 2nd March 1942 unfortunately this is a paywall.

5. The Jews of Japan ~ Daniel Ari Kapner and Stephen Levine

I think to answer that question it is necessary to differentiate between three problems.

"…the Japanese would want to fight for the Axis": how was it, that Japan entered into the Tripartite Pact with Germany and Italy? What process led up to that decision?

"…the belief that… Aryans were the superior race": What was German political ideology? How did the concepts of racism and Aryanism concretize in society?

How did these beliefs influence the Japanese, how did they react to the racism of German nazism? While the first point does mainly concern political history / the history of events, the other two pertain to the field of intellectual history and are therefore, imo, way more troublesome. To engage in intellectual history means to construct significant currents by picking examples out of the vast corpus that constitutes what we see as 'culture'. Modern thought shows a confusing plurality, and the question of "who reacted how" is often best answered by generalizing about what milieu reacted in what way. That said, lets get to the first point. 1. The negotiations to form an alliance between the three 'late-comer nations' Germany, Italy, and Japan was a German initiative of 1938. The Japanese side was fully aware that such an alliance could have a negative impact on the Japanese relations with the Anglo-Saxon powers, and meant a high risk if Japan agreed to take military action when one of the partners was under attack. One crucial point here is, obviously, what does constitute an 'attack' (or, for that matter, war). Initially, the Japanese side saw the alliance as an extension of the Anti-Komintern, the anti-communist alliance that the three nations were already part of. While the civilian government officials didn't see such an extension to the realms of military commitments necessary, the army was behind the project. That had to do with the strong pro-German and sovietophobic (is there such a word?) feelings in the army (Drea has some great chapters on these relations in his 2009 book. The sentō kōyō and hohei soten 歩兵操典歩兵操典, japanese military manuals, had German ones as their model, and many important officers had studied there).

But then, in 1939, Germany effected a treaty of friendship with the Soviet Union. That made, as you see clearly, no sense to the Japanese. The Tripartite Pact was supposed to be anti-Soviet, thus Hitler's turn in foreign policy was betrayal, in essence. Therefore, the negotiations cooled down and as good as ceased. How was the pact concluded, then?

The 22nd of July, 1940 marks the start of the 2nd Konoe-cabinet. Prince Konoe Fumimaro is the leading figure in Japanese politics at the time. He is probably best characterized as a moderate conservative. Konoe selected as his Minister of Foreign Affairs Matsuoka Yōsuke, a candidate that close associates of his had warned him about for he had radical tendencies. Konoe believed that Matsuoka, who had been head of the Manchurian Railway Company before, had great political talent, and could help his administration in a time of unprecedented crisis.

This crisis (as you probably know, but I'll just mention it anyway ; ) ) was due to the ongoing conflict in China (which had become an outgrown war since the incidents in North China and Shanghai in the summer of 1937) and the increasing independence of the army, at whose mercy the civilian cabinets of the time found themselves (this point is raised again and again in the diaries of leading politicians such as Konoe, and the preceding Yonai-cabinet failed among other reasons because of the lacking cooperation of the army (rikugun)). The army minister had to be selected from among active generals.

Another important point was the greater unity of the army, as the failed coup d'etat of 1936 made the 'control faction' (tōseiha) the dominant force within the army. In essence that meant the lack of a check on the 'control faction', giving it more leverage in political dealings.

Now Heinrich Stahmer visits Japan, it is the 7th of September, 1940. It is a time of great excitement, especially in the military: the reversal of the global power structures seems almost tangible, as Germany has triumphed over continental Europe in its stunning campaign, lasting just a little longer than a year. Stahmer then brings up the issue of the pact again, and Matsuoka, supported by the army and the mood of the general public, sees to Japan's joining the axis. But that did not go unopposed. The Emperor of Japan had voiced his opposition to the pact from the beginning of negotiations, strongly criticizing Gen. Itagaki, Army minister at the time. Prince Konoe relied on Stahmer's guarantees of good German-Soviet relations, rendering war between the two states 'very unlikely'. The irony of this statement is obvious.

What does this tell us? The axis seemed certainly desirable to an army thirsting for war and a restructuring of power in Asia (I think, this is not too ambitious a thesis). The civilian government, however, was not that convinced of its merits, and many ordinary Japanese probably weren't really seeing the meaning of it, regarding it merely as an alliance of countries with a common goal of challenging the current world order. Besides, it is not clear if the axis was of that great importance. Koltermann in his 2009 book points out, that the axis power distrusted each other, and that neither the Japanese military nor the German generals developed really any passion for the project.

One prominent exemption is the Führer himself: 1945, defeated, he orders U-Boote to ship advanced German aircraft to Japan. The only chance for cooperation was missed through German arrogance and Japanese disinterest: a coordinated attack on the Soviet union took never place. Thus, the axis was based on a common feeling of related character (ein Gefühl grundätzlicher Wesensverwandschaft, as Koltermann has it) rather than tangible material merits. btw I am sorry if the treatise is confusing from time to time, I am just typing away. : )

Now, to the 2nd point. It is in essence the question of Nazi ideology, and the literature on that topic is vast. A prominent example cited very often is Rosenberg's "Der Mythus des 20. Jahrhunderts", probably second only to the many many analyses of "Mein Kampf". I will raise only a few points here, that may get us to a better understanding of the issue at hand. Racist ideology was no unified concept. Though the Aryan as supreme being is a common trait, the position of other races, and what followed from these concepts, differed quite significantly. Rosenberg, f.e., dreams of a racially separated world, and rejoices at the thought of an autark Asia freed of European colonialism. If the Jewish element has to be physically exterminated is, on the other hand, an answered question to him. Hitler's positions are contradictory. He does not concede to the Japanese the same rank as to the Aryan (who is 'Kulturschöpfer', the author of the world), but he puts them in a kind of 'middle category'.

Hitler himself later discarded "Mein Kampf" as mediocre, a product of the Kampfzeit without relevance (Speer notes these remarks in his diaries, adding that they were the reason he never undertook it to read this NS'bible').

What level of discrimination did the Japanese face, then, in Germany? From the many reports of Japanese having been to Germany, we rarely hear any criticism. After all, the age is a racist one. The US anti-Asian immigration laws are way more present in the Japanese mind than an obscure passage in 'Mein Kampf'. At that, Germany was no colonial power in East Asia, and never had been a major player in the game, anyway. I refer again to Koltermann, who evaluates the German populace's attitude towards the Japanese as friendly and even admiring. The Nürnberger Rassengesetze were even amended to the point that Japanese were 'nicht minderwertig', 'not inferior'. Thus, the Japanese did not have a condescending counterpart in the Germans. The German ways of racism rarely had a negative impact.

That no nationalist Japanese would have acknowledged the superiority of the Aryan, however, is obvious. He had his own ideology of superiority, embodied in the kokutai. But that did not mean one had to fight with the Germans over who was truly superior. Ideology does not deal in the business of logically exclusive scientific truth.

Coming to the third point, we can connect an interesting point to that argument, that will shed much light. Was racism as a model of thinking common to the Japanese, and did they therefore have no problems with the German ideology?

Adachi Buntarō is a name given by Dower in his famous study on the 2nd world war as a race conflict. Adachi, in a 1944 book on human anatomy, simply adopts the European methods of racial comparison, concluding the physical inferiority of some features of the Asian race, but by no means all of them.

Nagai Hisomu is cited by Szpilman in an article in the 2006 publication "Japanese Fascism" (the book tries to make the case for applying the concept 'fascism' to Japan, which I am no big fan of, but that would lead to far in this context). Nagai is a scientist of eugenics, and a truthful believer in the optimization of the racial stock of a nation. He concludes his articles with "Hairu Hittora" (Heil Hitler), which does hardly surprise. During the 30s, he leads his own institute lobbying for eugenics.