You are right. But it is not a matter of who deciding what. As you said, China has borrowed or integrated many other cultures into its own social fabrics. It is a large capacity of doing so. However, it has its own unifying agent, which makes Chinese culture a distinct one, though always shifting. It is Chinese language. The only foreign cultures that will be adopted or integrated are those that present themselves in Chinese. Even foreign rulers who wanted to make their rule last had to adopt Chinese. Buddhists knew it. Christians knew it, too. Many very enlightened Buddhist masters strove to translate Buddhist scriptures from Sanskrit to Chinese. Their translation is so brilliant that it is now a part of Chinese heritage. Christian missionaries did the same, though not as lucky as Buddhists. Doesn't matter where a culture was originated, China can absorb into its own when it sees its brilliance. But it has to wear Chinese clothes. Even ruthless conquest could not make Chinese to bend this rule.