After 32 generations (~800 years) you have more genealogical ancestors than there are base pairs in human DNA. There literally isn’t enough resolution to store a “record” of each of your ancestors, even if you inherited exactly 1 base pair from each ancestor.
Additional complications make it an even shorter timeline. After about 8 generations, you share no more DNA with your ancestors than you do with a random stranger.
Politically this should be more well known. Of course, racists and fascists rely on “blood quantum” arguments to justify racial or ethnic oppression. But they don’t invent this idea of strict genetic identity. It’s latent in the population.
Leftists should more frequently call out genetic tests like 23andMe as inherently racist because it’s based in race science nonsense. It may not be as obvious as Nazis invoking aryan genes or whatever; but it’s still just as incorrect when your aunt at Thanksgiving talks about how she discovered she’s 2% Choctaw or whatever
The keyword is each. You still have DNA from many of them. Plus DNA based ancestry works with key genes. A male has his father's Y chromosome, who has his father's Y chromosome, who has his father's Y chromosome and so on. The same goes for mitochondrial DNA through the maternal line. There are mutations of course, but those actually allow you to paint an (imperfect) timeline and create groupings (haplogroups). Men from Europe have more similar Y chromosomes to each other than to men from elsewhere.
Obviously none of that justifies racial or ethnic oppression nor indicates any significant differences between peoples, but it does allow for those trivial (as in, interesting bits of information that aren't all too useful otherwise) but imperfect groupings.
I don't know how the exact percentages are determined and I'm sure there is something closer to race science bullshit in there, but it's mixed with actual science. It's pretty simple to see for example that my mitochondrial DNA aligns more with people from Iberia while my Y chromosome is much more like men from England. Thus I am half Portuguese half English(-descended American). But it means absolutely nothing other indicating who my parents are. That of course tells you nothing about my intellectual or physical abilities or any predispositions despite what fascists claim.