Correction: Xi and the CCP have their own culture and mores
The people, though, want to see The Big Bang Theory uncensored.
The people are different from Xi. They don't want the same things as he (except for the ones Xi has successfully brainwashed, or those who have a highly tribal brain).
> why should it allow that kind of soft projection
That sounds paranoid, I hope you don't mind. Reasoning in that way, almost all movies in the world wold be a "soft projection" and Nation State attack. But sometimes it's just jokes or reality and a good movie ... or would have been.
I mean, I don't think it requires any sort of active attack, or paranoia about a malicious attack, to recognize that soft power is real and it can influence people's behavior even when nobody intended it. The Big Bang Theory, as a reflection of American culture, can work to perpetuate that culture and serve America's interests even without anybody in America or anybody working on the Big Bang Theory intending for that to happen.
Now, in the case of the Big Bang Theory, whether that is good or bad is somewhat up to whether you think American-culture-as-espoused-by-the-Big-Bang-Theory is good or not, but honestly as an American who generally thinks American culture is good about some stuff but not everything, the Big Bang Theory is pretty far down on the list of cultural exports I would consider good or important. There's a lot of stuff in the Big Bang Theory that I feel ashamed to be associated with, including some of the stuff mentioned in this article as cut, like the racist jokes about Chinese people.
On an individual level it is obvious that almost no one advocates for self-censorship. Most people are only enthusiastic about censorship when they are the censor and not the censored.
The communist dictatorship is a parasitic form of governance, but most cannot escape because they're stuck at a local maxima.
Most people don't like being censored themselves, but don't confuse that for a moment with believing that most people want everything uncensored. For all public discourse in America constantly talks about free speech absolutism and the horrors of censorship, US TV has "decency" regulations and there's absolutely no mass movement to ensure that TV companies are not penalised for 'wardrobe malfunctions' and expletives are broadcast without bleeps. Why would people from a much more conservative culture where public discourse attaches no value to free speech but stresses paternalism and patriotism instead be so keen on hearing alleged rudeness about their country?
These discussions conflate voluntary censorship like age-gating with willingness to actually let someone lie to you, even in cases where you know the truth directly, and accepting it - ostensibly for the good of the group.
But when the indoctrination collides with reality in a harmful way, it's a different matter. Objectively, it is true that gay people exists and that there is no good reason to restrict their rights.
It's a deeper level of indoctrination. When these things are covertly inserted in an innocuous sounding show, not only will you start thinking about them, you will subconsiously think of them in a tolerant light.
China has its own culture and mores, why should it allow that kind of soft projection of Western power.