On a macro-scale the non-Han are relatively small, though, especially compared to some of the other cases of multi-ethnic countries. Non-Han-Chinese make up only 8% of the PRC population, whereas non-Russians make up about 20% of Russia's current population, and made up about 40% of the USSR's.
It is true that they're much more prominent in the outlying areas; e.g. 60% of Xinjiang is non-Han. Those areas have relatively few people compared to the more populous parts of China, though; Shanghai alone has more people than all of Xinjiang. China's current strategy seems to be to take advantage of that numerical imbalance to Han-ify the outlying areas, since the smallish (in absolute numbers) non-Han population can be swamped by moving only a few percent of the people from the central cities out there.
It's easy to throw out numbers like 8% until you realize that it represents over 100 million people. Per capita that may be a small number, but in the general scheme of things it means a lot of disgruntled people. I never really thought about it until I went over there and had the chance to interact with various groups, and it changed a lot of my perspective on how China functions on the inside.
I grew up in Xinjiang, arguably the most ethnically divided region in China, so I know where you're coming from. China's approach to taming ethnic minorities is straight forward: various forms of oppression. Besides racism, the other major reason is that minorities in China, unlike those in the US for example, do not want to be Chinese. There's no civil activism because neither side want true equality (both want to be separate).
Back to the original point: the Han peasant class is far greater than any other demographic. That demographic has been responsible for the dynastic cycles for thousands of years. It's still the case today, and the Chinese government is well aware of that. At the same time, the government has to keep stoking the economic fire, promote innovation, etc.
It is true that they're much more prominent in the outlying areas; e.g. 60% of Xinjiang is non-Han. Those areas have relatively few people compared to the more populous parts of China, though; Shanghai alone has more people than all of Xinjiang. China's current strategy seems to be to take advantage of that numerical imbalance to Han-ify the outlying areas, since the smallish (in absolute numbers) non-Han population can be swamped by moving only a few percent of the people from the central cities out there.