"Furthermore, in practice it is not enforceable, since you would have to know someone's entire ancestry to know whether they were eligible to marry another person."
Not true! Knowing someone's entire ancestry since the beginning of H. s. sapiens may be impossible, but less-rigorous standards of discrimination are practical to implement.
Nazi Germany defined how Jewish someone was based on their number of Jewish grandparents. This means checking genealogical and religious records back two generations. I've heard that some positions, like the SS, required proving your ancestry back to 1750. I don't know how many people were certified, or how extensive the research was -- could someone walk into an office with a few badly-copied baptismal records and get their "I can marry a German" card stamped? did it require checking government databases? -- but it must have been a large number.
The existence of terms such as quadroon and even octoroon show that people of centuries past seriously considered and even legalized notions of how 'black' people were, but I have no idea how well-implemented they were in practice. (I imagine there was a lot more "yeah, you look white enough" and a lot less "please come back tomorrow after I've telegraphed the Census office".)
My brain kind of needs a shower now.
Edit:
My knowledge of these subjects is limited to about 90 minutes of reading Wikipedia, by the way. I was vague enough that I don't think anything I stated is actually wrong.
Incidentally, apparently Nazi Germany had a scandalous number of women who suddenly admitted under oath that their children were the product of an extramarital affair with a conveniently non-Jewish and dead family friend. How well this worked may have depended on how well-connected you were. The senior Luftwaffe officer Erhard Milch is a prominent example.
Edit again:
If your point was "in practice it is not enforceable", mine was that it was enforceable enough that a lot of people put a lot of effort into trying, even if they didn't pull it off perfectly.