An advertiser may care about more than one of these things at a time ("interested in baby wipes" + "what culture do they identify with" so I can target things culturally, for instance), but even a very highly-targeted ad will be ignoring all sorts of attributes.
If you are really applying attribute tags to individuals, you are not "grouping" them in the usually-understood meaning of stratifying.
In truth, you are still building an individual profile for each person, but describing it in a disingenuous way.
Under most circumstances this would be a distinction without a difference, but in this specific case it turns out to be important. If advertisers are interested in "groups" than they may still think of themselves as needing identity, and demographic breakdowns, and wanting addresses for those groups, etc... but if you conceive of all they care about as being "in the market for baby wipes" there is no reason to give advertisers anything more than "here is an advertising opportunity for baby wipes", and no other information. Not an aggregation of "individuals", with all the extraneous baggage that comes with, but aggregations of fine slices of attributes that they have no need to correlate to anything else. (Only residual desire because they're probably still used to thinking about "individuals".)
>there is no reason to give advertisers anything more than "here is an advertising opportunity for baby wipes", and no other information.
That's exactly what advertisers are offered. Do you believe otherwise?