u/vnth93

You may have heard of this idea. This writing is not intended to settle the question, but to establish what this position is and clarify some of the misconceptions surrounding it.

I can only address the scholarly hypothesis. I am aware that there are various versions of this floating around on the internet, especially the Chinese internet, which are usually treated by Chinese netizens as anti-Chinese or Turkish nationalist conspiracy theories. And this, in turn, gave some people the belief the hypothesis itself is nonsense. To my knowledge, it is still relevant in Western scholarship. If you want to read more, see, for example, Sui-Tang China and Its Turko-Mongol Neighbors by Jonathan Karam Skaff and Middle Imperial China, 900–1350 A New History by Linda Walton.

Some elements of this have a very long history. The claim of the foreign ancestry of the Li clan was fairly well-known during the Song dynasty, being repeated by the likes of Zhu Xi. Some Song literati considered the Li family to be barbaric with many corrupted foreign practices, in other words, un-Chinese. It was only in the modern time that the claim is considered anti-Chinese.

1. What this is about? Chinese traditional histography emphasized the Han-Hu distinction between the China and the various nomadic realms. Modern people often co-opted this to retroactively assert it as an ethnic distinction, as in China has always been a distinct nationstate being threatened by foreign invasion. Recent scholarship, more so Western scholarship, explored the interconnectedness of Northern China and Inner Asia, to the extent that they can be treated a a single entity. The Tang dynasty was obviously cosmopolitan. The question then is whether it can be considered a multiethnic empire or a Han empire with multiethnic elements. Traditional history erroneously asserted that Tang invented Chinese style cosmopolitan rulership, when, in reality, many of its practices were inherited from Northern Wei, which was undeniably a multiethnic empire.
2. Turkish? Li Yuan's family carried the Xianbei surname Daye. There is an argument over whether he was from a Han family that underwent Xianbeification during Western Wei, or, a Xianbei family underwent Sinification during Sui. A 6th century monk named Falin was the first who suggested the idea that the family was descended from Tuoba clan. At the time, and for a long time afterward, the Tuoba was considered Xianbei, who were originally a "Donghu" or East Mongolic people. Modern language studies suggest the name Tuoba may be Turkish in origin, which also leads to the proposal that the Xianbei might have become a multiethnic confederacy at some point. In any case, whether they were Turkish is actually unrelated to the Xianbei claim. The Li family's ancestry itself may be connected, but perhaps not mutually exclusive, to the cosmopolitan policy of the Tang dynasty. It was probably the simplest way to explain it.
3. Mixed-race? According to the traditional Chinese worldview, a person's "stock" is paternal. From a historiography point of view, political power was primogeniture in nature, transferring from father to son. The attested Xianbei's identity of Li Yuan's mother (and also of Empress Zhangsun) is then entirely irrelevant to this debate. The family was not mixed race in the modern sense and the idea is not significant in any way. They were not Xianbei because of this, if they were Xianbei at all. Certainly, regardless of the true patrilineality of the Li family, they had never bother to hide the fact that they intermarried with the Xianbei aristocracy and this did not affect their professed Han identity. The question is only whether the Li family was a part of the Xianbei aristocracy themselves.