You are thinking of open in-your-face racism like calling people "stupid chink", "dirty chinaman" or whatever. Of course, that is not really common.
What is the most troublesome is the insidious racism that Chinese face. The most common one we see around the world is related to property/real estate ownership. Basically every western country is complaining of Chinese investors buying up properties, driving up prices, and basically taking the land away from "True Americans/Canadians/Brits/Australians etc."
The question nobody is asking, why is this seen as "wrong"? Because the sad, simple answer is racism.
Why shouldn't Chinese people be able to enjoy the fruits of their success? What is wrong about that? Is that not the essence of the capitalist system? In an export driven country like China, their success is driven by the consumption in western countries. The Chinese glass factory owner is rich because of all the iPhones being purchased every single year, it is not nefarious or dishonest.
So the next step is the media twisting some other stories to make them seem more "evil". They are exploiting children, ethnic minorities, destroying the environment, etc. etc. Do we ever really ask an average person, "What do you think is going on in China that XXX is happening?". Taking child labour for example, people seem to have a comic book perception of what is going on. Like the Communist soldiers going into a village and rounding up the children to go work in a factory. Not the much tamer reality that these kids are from poor families and factory wages are decent. Is the manager an evil taskmaster looking to exploit children? Or perhaps they look the other way because they know the life back home for them might be worse? I am not condoning child labour here, just throwing out a hypothetical that people don't often consider.
So we have so much time and effort spent to shape this idea of how evil China is, but then just because you say "but you know, not all Chinese are like this", and it's supposed to make everything okay? If I drive a nice car around, are people more likely to think "Another rich Chinese asshole", or "a fine example of a local born kid of hardworking immgrants"?