China’s fight against religion and culture is about control. This is due to their modern support of Communism, which tries to eliminate every threat to its ideology (it cannot survive otherwise). That’s why texts on Communism and Socialism often call for the elimination of religion, family structures, etc. It’s not about fighting a “cult” for some virtuous reason. If anything, authoritarianism and Communism are cults, and the Chinese version was visible clearly in the cultural revolution (https://en.wikipedia.org/wiki/Four_Olds). I’d also note that the absence of religion isn’t cult-free, and there are many cultish movements in the world even from non-religious parts of the world.

From the Chinese perspective pre-Communism, there would be no issue with Tibetan culture. But even if there were, it isn’t for them to care about or interfere with right?

As for your other comparisons. I don’t see cannibalism or Islamic fundamentalism (Jihad) as being comparable to Tibetan culture. Islam has explicit calls for violence against other belief systems. Tibetan culture does not. I can see treating Islam as a threat because of what it states openly, but it would be weird to group that with Tibetan culture, whether before or after Buddhism.