I can see that people often get worked up when the issue of "race" and "human genetics" is mentioned.
My advice is: RELAX!
By discussing what the founders of the Gokturk Empire looked like physically is a trait of curiosity, which doesn't necessarily imply racist or nationalistic propaganda.
The same way I have always had a curiosity to know what people "looked like" at different eras and different places.
I am curious to know how the ancient Italians "looked like", how the Cro-Magnons looked like, how Neolithic people and Jericho and Catalhoyuk "looked like". how the Aztecs "looked like".... and it's only normal for people interested in history and geography.
The terms such as "Caucasoid", "Mongoloid", "Congoid" or "Capoid" are broad classifications of craneology, which DOES EXIST in a broad sense; which is just as valid as dividing people into blonds, brunettes, and redheads when it comes to the colour of the hair. Most of the time you don't tend to confuse a typical Chinese with a typical German, do you? So there IS a physical difference between the 2 peoples; and there's nothing racist or nationalistic about admitting it.
I can blatantly say that even among Europeans there are physical differences, as a typical Spaniard DOES NOT look the same as a typical Swede; and there's nothing racist about saying it.
The word "race" is another matter because in animals it means "subspecies"; while all human beings alive today belong to the same species and sub-species. However, there IS genetic differences between populations of the world and there's nothing racist about studying them. Just because the racists of the 19th century used the colour of skin as social divider, it doesn't render the study of genes and "looks" irrelevant.
Going back to the main topic, I would imagine that most of the original "Turkic" tribes that descended from Xiongnu were probably of Siberian-Mongolian heritage; but by the time that the Gokturk empire was created, they had already absorbed a large number of foreign peoples of Iranic, Mongol, or Finno-Ugric origin.
Their physical appearance was most probably mixed.
An Lu-shan was a Chinese general of Turkic origin, and historical sources did mention him as "physonomically alien".