It does not follow. Race itself (since you're using 20th century fascism, read: Nazi) is a singular aspect of diversity. Organization is a poor selection of term, too. Institution is better suited.
It doesn't matter how you mince it the only truly homogeneous populations are at-risk marginalized nomads. With that framed: you can find greedy, lecherous, exploitative, amoral or immoral slouches in every corner of the Earth regardless of race, you can equally find people that you'd invariably frame as noble, selfless, vulnerable understanding humanitarians... and we can fairly posit then, from every race, creed, region and religion you can pull from these pools any imaginable quantity of the human spectra - and I expect anyone else would, and they would elect people deliberately close to their own beliefs and goals because it's necessary to have some alignment within any large organization and especially a society. In fact there's something to be said for religion to affect this conversation, and it's that it permeated every early civilization - and one would rightly point out that's because values were made concrete and "objective".
Now I expect you didn't consider it, but there are a lot of groups that don't share your values. They feel very strongly, to the extent they would kill you and dismember you over it, some would just kill you, maybe torture you beforehand. I mean, that's really diverse is are those individuals you'd want in your institutions? I expect no. Likewise there is not necessarily some imminent moral concern that doesn't at least parallel that: some people don't want to be around other people - values collide because ultimately we live in a relativistic world.
The real problems you described can be chalked up to a few things:
The state: Monopoly on power, disempowers individuals, individuals relinquish their moral obligations including refusal to participate
Nucleated power: Institutions are supposed to act exemplars of behavior, instead they simply are exemplars and people follow, and then more follow suit. Suddenly the Third Reich is marching on Poland. Purpose and moral delegation is performed by institutions that are, due to human limitations, intrinsically unsuitable for the task. Obviously there is the element of controlling incalculable resources like every competing power in WWII had which emerges from this...
Limited options: Individuals and communities are unable to disband from their respective state apparatus e.g. secession due to the imminent threat of violence, retaliation and/or a complete lack of peaceable legislative or political option.
Scale: Dunbar's number, hypothetical maximum of about 150 people for functional human communities. When a neighborhood school in rural America doubles that easily, one is left to wonder how an institution deals with that, it's by mishandling every human it deals with. Catch-22's and C.S. Lewis's hell. People are abstracted into cattle (see Eichmann) or mechanisms in a greater machine, expected to go flawlessly whirring away without question or complaint at the throw of a lever.
It doesn't matter if my friend group is a contractile 10-man squad because we all came from different backgrounds and currently live entirely disparate lives. And we're from one of the most demographically and politically homogeneous states in the US and not one of us has similar views. We're irrelevant because everyone defers to the clueless state, for one, for two we're 10 out of a denominator of millions of hundreds of millions.
The problem is with institutions, and hierarchy, and bona fide power, and the concepts of property on which they're founded which again, circularly is a reference to the deference individuals must grant the state which makes it all fall into disproportion. Nazis couldn't work to found a kingdom without people to participate in their game.
I elected "institution" because there are a lot of voluntary organizations, but an institution is fundamental and intersections with them are inevitable. My friends, my [hypothetical] church, the workout classes organized by some nice lady, the food bank, salvation army... Individuals have mobility and they're able to reject or accept. Institutions your workplace and government - by dint of being necessitous - drastically reduces one's degrees of freedom, limits their mobility, and entraps them to varying extents. That's a real problem. If I don't like Nicaragua they can arbitrarily refuse me a Passport so I can't leave, forcing me to work at a sweatshop, and then the government can hold me at gunpoint to take some fraction of my infinitesimal income.
Anyways, there's different strokes for different folks and there's just as big of a proportion of any "minority group" in every corner of the world that would just as soon self-segregate so they can attend to their communities as there are people who want to live in "diverse" communities in accord with their values. And there's also a lot of performative white guilt bullshit from people who won't bend their ear to a black man, but will naively attempt to run to his "defense" at every opportunity. It's disrespectful.