Interesting theory, with some foundation, but I’m going to ride to the defense of our mostly gallant crew and use Vera to shoot it full of holes. Sorry, but you can’t come at the Captain like that. . .
The crew demonstrates time and again that they are MOSTLY decent people. The jobs they take hurt no one but the Alliance, and when they accidentally take one that does hurt ppl, they go up against Niska to make it right. They take a job keeping bandits from stealing from honest farmers, Magnificent-7 style. The protect a whorehouse from a rich bastard, for next to no pay. In the movie, they agonize about having to leave a townsperson to die at the hands of Reavers, and are outraged when the Alliance killed a whole planet with Pax. Mal won’t take advantage of YoSaffBridge, even when she was. . . so. . . very. . . tempting. These don’t seem like the sort of folk who harbor a dark, genocidal secret, and if they hate Chinese people, why do they make such flowery use of the language when angered? You’d think they’d reject the language along with the people.
It’s not EXPLICITLY stated, in terms of a declaration of secession or anything, why they fought the Alliance, but time and again, it’s stated the Alliance were meddling, looking to impose themselves on the outer worlds. People shown to be part of the Alliance, by and large, aren’t good people, and the more money and power they have, the worse they are. Simon’s parents are assholes who worry more about their reputation than the well-being of their young daughter, and they seem to have no regard for the brilliance of either of their children, totally disregarding Simon’s deciphering of River’s code. They are cold, self-centered people.
The Alliance looks to impose order above all. The movie caps off the series, showing the development of the experimental Pax drug to pacify populations, but that killed more than 99% of the population and turned the rest into crazed Reavers. They want to make a perfect world - all of them. THEIR idea of perfect.
We’ve remarked in this thread about how similar the names Browncoats and Brownshirts are, but maybe take notice of the grey-black, Hugo-Boss-looking uniforms of Alliance military officers.
Given what else we know from the series, it seems much more likely that Joss made use of tropes. He borrowed the Confederacy’s “brave soldiers fighting a lost cause” trope for the Browncoats. He looks to have borrowed expansionism, order, control and the quest for perfection from Nazi Germany for the Alliance. He probably borrowed from other sources I/we haven’t noticed, or perhaps would have borrowed from them given a full series run. This doesn’t mean they were, any of them, direct stand-ins for anything or anyone in history. He just picked up some tropes and used them for his own purpose. They’re good tropes.
Finally - and most importantly to me - knowing what the series endgame was (the secret of the Pax and the Reavers), how would have making the Browncoats genocidal served the story? Now we’d have genocidal ‘good guys’ fighting Nazis. How would that even work, and who would watch that? Don’t give in to an M. Night Shyamalan twist just for the sake of a twist. It’s messy and pointlessly slops up a perfectly good plot.
I never come up with cool headcanon for anything, and I’m jealous of folks who do. I’m sorry to poke at yours so much, but you came at the Captain. . . 
God, this is long. This has turned into one of those, “There’s something WRONG on the internet!” situations, hasn’t it? 
I do wonder why there were so few Chinese people, though. Maybe I’ll take a shot at this headcanon thing.
Perhaps there weren’t an equal number of Americans and Chinese, and/or, early on, disease or disaster took many of the Chinese. They were around long enough to make an impact on the culture and language, but a large chunk were removed from the gene pool after just a few generations in the new system. Much like people do now(Chinatown, etc), they each mostly clustered together in different settlements, and so many Chinese could be killed all at once, leaving a relatively small amount that had lived with the Americans. Maybe an asteroid hit? A terraforming accident? Disease? An accident on the ships as they traveled to the 'Verse? Possibilities abound when settling a new solar system. In this scenario, it could have just as easily been the Americans that took the hit, but it didn’t work out that way.
Thank you, and good night. 
