Yes, there's variation within groups. But there are only a few mutations for digesting lactose, and much of humanity can't handle fresh milk after age 4 or so.
Variation within groups is considerable, but that doesn't mean there can't be nifty cladistic analyses done showing how human groups split genetically (and sometimes later mixed or were submerged as another wave of humanity washed over them).
Studying that kind of "divisive" genetic variation isn't popular. It's deemed as supporting racism, esp. when some of the variation confirms those generalizations based on partial observation called "stereotypes." I think of it as "prototype theory"--there's the "ideal" phenotype for a group with a narrowly characterized genotype behind it, and that accounts for most of the population. Then there's the outliers that provide the variation. If you just focus on the amount of variation you miss the big picture.
The genetic variations I've run into were mostly accidental or incidental. I spend years interested in historical linguistics and things like homeland studies. You can look at language-internal stuff, words for "bronze" or "salmon" (for PIE) or similar kinds of words for Bantu languages or Austronesian languages. You can look at archeology and trade or migration patterns. Or you can look at cladistic analyses, many of which based on a completely different kind of data look startlingly like reconstructed language trees. Then you can look at the differences or compare them with the archeological record. (And, no, I think that most biologists/geneticists' clade-based analysis of language history are simply bone headed, based on facile comparisons or clumsily assembled data sets.)
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