You're 100% right about the point that the ordinary Chinese person does not feel oppressed by the Chinese government, and they have every reason over the last 30-40 years to be bullish on their government given how many people have risen out of abject poverty in that time (sure, it was poverty that the government helped orchestrate in those preceding years, but still).
I think that the social credit system is similar to the Trump administration's policy of detaining immigrants at the border, they're both types of 'canaries in the coal mine,' in that they're a good representation of general anxiety that other people have about the government. China's crackdown on Muslim minorities is, by far, much worse than the 'social credit system,' but both of them are emblematic of the same thing: A super-powerful surveillance state, and the crackdown on Muslims in West China is what many would see the fruition or culmination of the technology behind the social credit system in the more populated cities in the rest of mainland China.
Millions of Americans were skeptical of the Trump Administration's appeals to far right ideology, Trump's coziness with foreign dictators, and they're skeptical of the relationships that Trump makes around the globe. Many Americans see the Trump Administration as a sort of wanna-be fascist administration... But, the overwhelming majority of Americans have not had their lives materially changed over the last 2-3 years by the Trump Administration. Except (and others) can point to the border dispute to see how the Trump Administration treats the most vulnerable, they lock them in cages, separate children from their families, and give refugees and immigrants virtually no due process under law. So, while most Americans are materially unaffected by child separation at the border or policies locking refugee families in cages beneath bridges, it's a sort of canary in the coal mine that shows you the true character of this administration.
With China, you can look at hundreds of thousands of people being sent to concentration camps in West China for doing things like growing a beard, reading the Qur'an (or being accused of reading the Qu'ran), or talking with Western journalists, or talking to their children who are studying abroad ... and then you can also look at this vast surveillance state and how it makes these things possible. The same thing that makes jailing Muslims in concentration camps possible is the thing that makes the social credit system possible.
The main issue is the Chinese government, just like the main issue for many Americans is the Trump administration's daliance with far right fascism... But things like the social credit system or family separation of immigrants is the thing that people can point to to say, "See -- this is evidence of what their true inclinations are!" The social credit system may only unfairly ruin a few peoples lives, and in a country of billions of people, it's easy to say "What's the harm? It's just a few thousand people who have had their lives unfairly ruined by this?" And likewise, it's easy for an American who lives thousands of miles from the border to say, "What's the harm? These immigrants are crossing the border illegally so it's okay to detain them?" But, when you see nefarious ends -- as most of us do with the Trump administration or with the government of China -- these things that most people are inoculated from end up being representative of the true intentions of those who are implementing them.