Well, here at Stanford they put Indians and Japanese in different categories, but that's hardly the point. These groupings represent political categorization based on racial categorization. I had thought the tongue-in-cheek nature of my reply would have been more obvious, but I'll make it more explicit: those who most strongly advocate the "no such thing as race" position tend to most strongly advocate race-based preferences when it suits their political agenda without, apparently, seeing a hint of irony. When someone who denies that races exist demands to see my list of races, I suggest he try using the list of races used by his own political allies.
There are different races in the sense that there are different colors on the visible electromagnetic spectrum. There is no "correct" categorization on the spectrum itself, but you can observe clearly different clusters in many situations. Take all the red, green, and blue elements from several video monitors and graph their frequencies and despite that fact that there is a lot of diversity, there won't be a uniform distribution. Three clusters will be easily visible, and you can call them clusters red, green, and blue. In the application, unlike the theoretical spectrum, these categories do exist.
History has clustered human beings, too. Nobody here really denies that humans have descended in a complex tree with lots of crossovers. There is no right way to categorize all leaves of the tree itself into sharp "races". Even so, historical accident has resulted in a lot of clustering of genetic affinity where members of a cluster share lots of relatively recent common ancestors but have mostly very distant common ancestors with members of other clusters. The fact that there are individuals of all sorts on the human tree doesn't mean that there is no clustering.
So Han Chinese, Central American Indians, Northern Europeans, and West Africans diverge long ago and don't intermix genetically for a thousand generations, then history brings them together recently in the Americas where they begin to interbreed.
Nothing wrong with that (at least IMO). Eventually this interbreeding may reduce the clustering to mere random clustering, but today there are still strong, clear clusters of genetic affinity. You can call the clusters races or call them foo, but they aren't just figments of the imagination. The admissions department at Stanford has no difficulty in most cases distinguishing an Indian from a Japanese by genetic affinity with other members of these groups. Whether they then make that two different racial preference categories or assign them to the same "Asian" group is just identity politics.