Original Han culture is from 2000 years ago. Of course Han culture would be drastically different today than it was 2000 years ago. The influence of the northern nomadic cultures on Han culture is insignificant compared to cultural exchanges through peaceful means such as trade. Buddhism, for example, came to China through peaceful means. Even if Han culture developed in a vacuum with no contacts with outside cultures, it would have vastly evolved and changes over 2000 years.
At the time period between the Jin and Tang dynasties, the concept of Han ethnic identity had not emerged yet. Prior to the Tang, the concept of non-Chinese cultural identities didn't really exist - there was only "civilized" peoples (Chinese civilization) and non-civilized peoples. Likewise, Chinese scholars never bothered to categorize different non-Chinese peoples by culture/ethnicity, and categorized groups of non-Chinese peoples together based on their geographic direction relative to China (ie Nanman, Dongyi, Beidi, Xirong). Once a group of people become "civilized," to Chinese standards, they were considered Chinese. China has been expanding and assimilating culturally distinct groups of people since the times of the Zhou dynasty. States of Qin/Chu/Wu/Yue are all examples of early Chinese expansionism and assimilation of outside cultures. Qin and Han continued this pattern of Chinese expansion and assimilation, until ultimately all agricultural land known to the Chinese came under Han control, from Vietnam to Korea. Ironically, the group that the early Chinese considered to be most different from themselves were the Southern barbarians, known as the Baiyue (Hundred Yue), which ended up being the group that was most fully assimilated by the Chinese. On the other hand, many Chinese sources at the time believed that many of the northern barbarians, were original descendants of earlier Chinese dynasties that had been overthrown (most likely untrue), due to their similarity in general appearance to the Chinese at the time. A Chinese peasant wouldn't really be able to tell the difference between a Xianbei in Chinese clothes from a Chinese hailing from a distant province. China at the time was a multi-ethnic state unified by a single cultural identity forged by the Qin and the Han dynasties. In fact, only after the Jin did large migrations of Northern Chinese move to Southern China, which over time would forge the Han ethnic identity. Even at the time of the Ming, many minority groups in the South such as the Zhuang, Liang, and Yao were considered indigenous peoples while the Jurchen were considered semi-Chinese.
Mass migration - ie northern Chinese to southern China - changed the culture and demographic composition of the region. I don't think this can be debated. The "southern barbarians" were assimilated into Chinese through this process. We all know this, and it's a great example of how much impact migration & conquest can have.
What you're trying to debate is that similar migrations from the steppe into northern China did not have the same effect, because it was the immigrants / invaders that were assimilated. This isn't entirely wrong, but it also isn't entirely right. Han ethnic identity was actually formed during the Northern Dynasties, in fact due to the practice of the immigrants / invaders of calling the conquered natives of northern China, "Han," by their destroyed dynasty.
So Han ethnicity began as a form of self-awareness in relation to alien peoples, who most definitely did not immediately assimilate. Indeed, this was not a great time for native Han; discrimination by the northerners is well-documented (look up Gao Huan telling the Xianbei nobles, "the Han are your slaves"), and for centuries the ethnic distinctions were maintained until finally, around the time of the Sui and Tang, it ceased being maintained.
But the culture and traditions of the north changed forever. Sui and Tang culture were not simply derivatives of Han culture; they were a mix of Han culture with northern culture, and this showed through in many aspects of life, from religion, to dress, to court rituals, to aesthetics, and to language. If you read history books on the period, you'll find records of how this change happened and how many influences northern peoples had on Chinese culture.
Simply blindly accepting narratives like "China has historically assimilated everybody" is naive. Yes, assimilation
eventually happens, but it's a mutual process, not one-sided
. It took three hundred years between the fall of the Jin in northern China and the rise of the Sui-Tang for Xianbei identity to stop mattering, and even then the new identity that replaced it wasn't the same as the old Huaxia of the Han. You can't expect China to import a hundred million Arabs or Africans or whatever, and for them to have no effect on Chinese identity long-term. That is just a fantasy.
The question you have to answer, as such, is whether you care more about the abstract political entity known as "China" or the demographic and cultural identity of "Chinese." Because the former can be expanded via mass immigration, but the latter can only be expanded via improving fertility.
