I grew up on a farm in South Africa, where most of the labour was either "coloured" or "black". When I read or heard of people who thought that effectively all unfamiliar ethnic types looked indistinguishable, I simply could not understand what they meant. They certainly looked just as distinct as "whites" to me, together with their own quirks of voice, mannerisms and character. Then I heard that all Chinese look the same. Well, in those days in that area there were not many Chinese but again, when I did finally meet ethnic Chinese (most of those I met were South African citizens, so I cannot really call them "Chinese") then I cannot say that they looked particularly hard to tell apart either.
Now, when it comes to animals, I do grant that if I see a group of wallabies or Chihuahuas of about the same age and size, and then I cannot really tell them apart immediately, but as soon as we have had much interaction distinguishing features almost invariably become painfully obvious.
At a higher level, in working with species of animals, in my experience typically insects, but much the same happens with reptiles fish and so on, I think that most biologists have had the experience of laymen being unable to recognise the differences between species that seem crashingly, almost painfully, obvious. However, herein lies a clue. I also have on occasion, mainly in my student days, being introduced to an unfamiliar species with a particular distinctive characteristic. There is a strong tendency thereafter thoughtlessly to identify any other species with the same characteristic as the same (by now slightly more familiar) species. This is a pitfall that catches everyone out from time to time, even if only for a short time.
What it seems like to me is that we learn, as a matter of efficiency, both in speed and effort, to identify individuals by their most salient features, and become almost blind to features other than those by which we distinguish them. This leads to the situation that when we have to deal with an unfamiliar population that lacks the distinctive features that we are used to, we suddenly find ourselves confronted with indistinguishables.
Now, you claim in effect that the variables we are familiar with in humans do not occur in animals.There are I take issue. I have never dealt with a macroscopic species in which I had any difficulty telling individuals apart, both by behaviour and physical peculiarities, once I got to know them. Certainly I sometimes might be fooled for a while, much as one sometimes says: "Hello Jack, how is Jill? Oh, sorry, I thought..." But it is a rare owner of say, two apparently identical dogs or cats (or parent of identical twins) that has any difficulty telling them apart.
Cats, dogs, horses, chickens, puff adders, Cobras, mantids, gouramis... you name it, they differ in their features as well as their behaviour; all you need is to learn the clues.
Frankly, I suspect that you too are just as able to distinguish individuals as most other people, just that you have not been put into a situation where you become aware of your own natural ability in this respect.