How could you? Any process and algorithm you picked for that measurement would be a prejudiced choice.

For example, if you used a human digital camera as your input, you'd be biasing based on frequencies human vision can see.

If your algorithm did some kind of hamming distance of pixels, it might be that one species cared more about that, whereas another cared more about a distance metric between fields of detected line boundaries. Who knows!

Any such attempt to quantitively measure variation in faces would also ignoring other senses, and other ways to establish identity than the face - just the choice of considering faces as an important discriminator feels anthropocentric to me.

In short, there is no definitive quantitative measure of "variance". That measure depends on both the senses and the brain of the observer - whether mechanical or biological.

Well you could physically measure the distance between the eyes, the curvature of the eye orbit, the width of the lips, curvature of the eye openings, length of nose, maybe a hundred such measurements, see how much each measurement varies between humans and then do the same test on raccoons. Wouldn't it be interesting if raccoons had similar variance in facial features but we just didn't know how to recognize them?

Of course facial recognition isn't the only way animals have of recognizing identity, but it's still an interesting question whether humans really have more distinct faces than other animals or whether we just think we do because we're really good at recognizing human faces.