Here's a thought...
I heard the Civil Rights leadership of the time supported WWII with the expectation of rights for blacks afterwards; that's one reason why many black leaders opposed Vietnam (we didn't get our end of the bargain last time), according to what I've read. I think Mohammed Ali asked "Why should I fight for a country that doesn't guarantee my civil rights" and he DEFINITELY said, "The Viet Cong never called me n*****".
Hmmm...what if the black leadership of the time decided not to actively push blacks to support WWII (more likely), or even declared for Japan (a non-white country fighting white colonialists). Perhap we have a different President during WWI who promises reforms (Wilson, a southern segregationist, would never do that, but someone similar might). However, reforms don't go fast or far-reaching enough (like in OTL) by the time of the actual war. Sort of like the situation between WWII and Vietnam, only a generation earlier.
"Solidarity" with Japan isn't so much of a leap, at least for the more extreme people who could arise. There's an old book called "Bloods" I found at the library about black soldiers in Vietnam and on its list of injustices they suffered (in addition to being there in somewhat disproportianate #s and mistreatment by white superiors) was that they were fighting "a colored enemy." I fail to see the moral difference in that regard (I feel little racial brotherhood with the Germans who killed my great-uncle in WWII), but others may disagree.
Of course, the person who wrote "Bloods" is probably more radical than the 1940s civil rights leadership, which I imagine was largely clergymen instead of bomb-throwers like the Panthers. However, actual large-scale declaration of sympathy for Japan is unlikely except AFTER radicalization of any sort of black anti-war movement, which could be caused by repression.
Owing to the domestic situation, a black opponent of WWII might very well be lynched or imprisoned (FDR put 13 "domestic fascists," which included several isolationists and even a pacifest Quaker in addition to the boss of the Silver Shirts, on trial for sedition at one point). Plus, something larger-scale could be tried...the US DID imprison Japanese-Americans.
Now, onto a better description of the scenario...
If even ONE civil rights leader speaks out against WWII (even in the context of Christian pacifism instead of sympathy for the Axis, just as King condemned the Viet Cong's terrorism as well as the US policy in Vietnam), all hell is likely to come down on blacks, esp. in the South.
This'll radicalize them and they'll fight back and THAT will radicalize whites and then things'll get really ugly. The Nazis could send some people to stir up whites and the Japanese could send some agents to stir up blacks and things will get REALLY REALLY ugly. It might end up like the New York Draft Riots, where soldiers have to be pulled back from the front to keep peace at home.
If it gets bad enough, you might be able to drag out the war for years or even have an Axis victory (assuming Lend-Lease is significantly affected enough to get Britain or the Soviets to make separate peaces with Germany).
I bet that's different than Nazis allying with the Klan, now is it?
No offense intended, Michael. I'm not claiming blacks are disloyal to the US or anything similar; I'm just wondering if something like the African-American opposition to Vietnam could occur (in a much less friendly and thus more radicalizing environment) during WWII.