Depends what you mean by fuzzy. it is culturally defined and people in different cultures use different definitions. Americans have whole categories not used in, for example, the UK (a very similar culture otherwise) such as "hispanic" which seems to include people I would call "white"? The same with people who are classified as "black" who look white. Americans now seem to use "caucasian" as a synonym for "white" which contradicts definitions used historically.

British people use definitions that are different from those of South Asians, and westerners in general are entirely unaware of caste which is a whole racial hierarchy that affects a lot of the world. Sri Lankans define race as whatever your father was, but Jewishness is inherited from your mother.

It might not be fuzzy within a particular culture at a particular point is time, but it is not consistent between cultures or over time.

Edit: initially omitted because I keep sharing it and might look spammy, but decided to add a link to my blog post on the topic: https://pietersz.co.uk/2023/08/racism-culture-different

When I wrote that I had in mind the idea of “mixed race” people. In the US it is very common for someone to identify as half black and half white, or one quarter Irish and three quarters Mexican, and so on. So, nuanced but not fuzzy, in that sense at least. But that is closer to ethnicity than race on second thought.