It's a test of the universal law that two random different things are never miraculously equal and never equal unless there is a spectacularly good reason.

That's not a universal law. A random partition of a large set of objects may well produce two sets in which the distribution of all properties is the same as in the original set. The same is true if the set is partitioned according to some property that doesn't correlate with anything else.

The controversies on this issue are about whether certain properties that can be used to partition human populations do have correlations with various other relevant properties, what is the reason for these correlations if they do exist, and what should be their wider implications.