Oh, we're well aware of that! Sometimes I think my wife acts racist, the way she acts towards FOBs (Fresh-Off-the-Boat or Chinese from Asia). She hates foreign Chinese not born here in the USA. And it goes both ways, the FOB Chinese show disrespect towards Chinese-Americans born here. Different culture, she thinks the FOBs are rude. Anyway, she was born in San Francisco's Chinatown, and her parents moved to a white neighborhood in SF when she was young, maybe 4. They only spoke Chinese at home, even though her dad had been here since he was a kid and was even in the US Army during WWII fighting in Europe for the USA, spoke English outside the home.
My wife was an IT manager of a large data center, and had some conflicts with Chinese employees. Because of culture differences, they couldn't stand working for a woman. One Chinese guy she fired did a lawsuit against her and the company claiming racial discrimination. The lawsuit went forward a while because my wife uses her married name (mine), then when lawyers found out she is Chinese the guy's lawsuit fell apart! Guy had to be dragged out of the offices by SFPD when my wife fired him. She became known as the Dragon Lady Boss because of that. She had white, black, hispanic and Asian employees under her, treating them all the same, although she disliked the Chinese guys and their anti-woman boss bias.
I've seen similar stuff in my job sites. One of the toughest managers was a Chinese-American gal from Texas, she took no crap from Chinese male employees and had them cowering in fear of her. I liked seeing her do that! On a different note, I've had many bosses over the years, and some of the most incompetent ones were either Chinese men or Black (both genders). Maybe I was just unfortunate, but I had better success with white bosses, again I'm generalizing about my experience.
Just my view of things. I ran a software company for 30 years. I had lots of foreign, mostly Asian employees and most of them are now citizens. When it came to the Chinese, they look at themselves as one in a billion. Those who get here have done it by testing into the top 1% and working very hard and having a great deal of gumption or in some cases they are the spouse of those people. When they meet your wife, because she looks Chinese, they are still competing with her. Its not too fair. Your wife knows all the rules. They don’t. Your wife understands America and Americans and users and bosses and laws.
But I don’t think its so much sexism that makes her have a problem with the Chinese men. There is cast in China. The two peaks of which are University of Shanghai and the true Shanghai accent. I watched one of my best Chinese male programmers cower to a Chinese women who went to The University of Shanghia. She wasn’t smarter, or better in any other way, but she was the creme de la creme in her own eyes. And the others seemed to agree that she was superior. I also ran into a Chinese guy who people would not eat with. They explained to me, he was a farmer. So of course they would not eat with him. The fact that he also had a PhD in Mathematics did not matter to them. We in America have sexism and racism but they have lots of isms that we have not dreamed of. From the south, from the country, from a lessor city, part of the government, dark skin, are all reasons for them to feel superior to another Chinese person. The interesting thing is that your children and theirs will happily play together with all those issues left behind.