Agree on the importance of history and culture as to why China maintains their particular political system.
China is also an enormous country - the western regions resemble very little of what most people think of "China" when they think of China, i.e. Han Chinese of the eastern coastal region (Beijing, Shanghai, etc). But we generally only hear about the Han Chinese because they are the ones who control the country; they also control the media so dissenting information is not readily and abundantly available.
For example, Xinjiang is culturally and historically very different from the culture and history of the Han Chinese - there have been lots of resentment and conflict in the region associated with Han Chinese rule.
So in a country as immense as China, it would be too much of a generalization to assume that the country accepts the current ruling political party flat out. We'd have to define what we mean by accept - accepting but secretly objecting out of fear of reprisal; accepting as a true believer; openly objecting; etc. - and where they accept it. But then, this becomes a difficult task, as stated before, the image we get of the country is heavily censored and curated - it is difficult to see clearly because of active obfuscation by the state.
Perhaps it's a combination of history, culture, state and media manipulation, ignorance of dissenting opinions in regions outside the core of Han Chinese China, nationalism and nationalistic pride, rejection of Western ideas and concepts tied to the humiliation of China by Western powers in the past, and I'm sure many, many other factors.