However, the genome can encode an initial crappy face detector.

It's not that crappy given that newborns can not only recognize faces with significant accuracy, but also recognize facial expressions.

The cortical map will grow a good face/person model/detector on it's own, and then after this model is ready certain hormones in adolescence activate innate routines that learn where the face/person model patch is and help other modules plug into it.

Having two separate face recognition modules, one genetically specified and another learned seems redundant, and still it's not obvious to me how a genetically-specified sexual attraction program could find how to plug into a completely learned system, which would necessarily have some degree of randomness.

It seems more likely that there is a single face recognition module which is genetically specified and then it becomes fine tuned by learning.

I highly doubt that - but it all depends on what your sampling class for 'human' is. An average human drawn from the roughly 10 billion alive today? Or an average human drawn from the roughly 100 billion who have ever lived? (most of which would have no idea what a parity function is).

Show a neolithic human a bunch of pebbles, some black and some white, laid out in a line. Ask them to add a black or white pebble to the line, and reward them if the number of black pebbles is even. Repeat multiple times.

Even without a concept of "even number", wouldn't this neolithic human be able to figure out an algorithm to compute the right answer? They just need to scan the line, flipping a mental switch for each black pebble they encounter, and then add a black pebble if and only if the switch is not in the initial position.

Maybe I'm overgeneralizing, but it seems unlikely to me that people able to invent complex hunting strategies, to build weapons, tools, traps, clothing, huts, to participate in tribe politics, etc. wouldn't be able to figure something like that.