It has long been known by humans that female mammals can be attracted with the call of a young in distress. There is a famous documentary film of the Hadza, a foraging group in Tanzania, in which this method is used by young boys to trap Dasssies (rock Hyrax). First you catch a baby Dassie (not hard) then you hid and bit it in the neck so it cries out, then when the momma Dassies come to rescue it you shoot them at short range with an arrow or whack them with a stick. Adult Efe Pygmy hunters sometimes imitate the call of a young Duiker (a forest antelope) in distress in order to draw in females. I've spent a fair amount of time hanging around with adult male Efe hunters and never saw this work, but they claim it does and I tend to believe them.
Now, researchers have demonstrated cross-species response to distress calls by young. They recorded distress calls by various mammals such as seals, dogs, cats, and humans. Never mind how they got the distress calls. Anyway, they played these for White Tailed Deer females and got a response. The mother deer moved towards the recordings. These baby mammals all have similar pitched calls. The researchers also recorded bats and lowered the pitch to be within that range, and the deer responded to this as well.
Presumably there is strong selection on responding to distress calls of young, but not strong selection on being selective, probably because the circumstances do not arise that often.
If empathy begins with maternal care, as Frans de Waal suggests, and if maternal care has existed as long as there have been mammals, more or less, then it seems a reasonable hypothesis that most females would respond to their own young. But responding to the cries of other mammals is fascinating.
I sometimes think that birds get overlooked in the whole empathy, care-for-young analysis. Birds are born dependent on adult(s) just like mammals are. As mammals I imagine it's easier to relate to mammalian behavior than avian behavior.
Birds are very important vis a vis parental care, and far more evolved than mammals. Ie, not as easily confused about who their offspring are.
There is probably a difference between herbivores and carnivores.
Maternal care has existed as long as mammals have. The characteristic of mammals is the mammary gland which is to produce milk to sustain young. All mammals have to exhibit maternal bonding, even mammals that are non-social (like bears).
Maternal care is the archetypal social behavior (in mammals). Pair bonding in female mammals recapitulates parturition and is mediated through oxytocin. Pair bonding in males recapitulates territoriality and is mediated through vasopressin.
That lends a bit of credence to all the stories of wild animals protecting the young of other species. There was a case last year in Ethiopia of 3 lions protecting a 12 year old girl who had been abducted and beaten by a group of men. Presumably the lions heard her crying and thought she was a baby. It's said they chased off her abductors and protected her for 3 days until she was rescued.
Probably those were lionesses in that case? It seems like females respond more than males, but not necessarily only if they are mothers. Hearing a cat crying anywhere within half a block can make me come running in case I can serve ... I mean help. I don't have kids.
I live in sheep country and can find the cries of lambs distressing so I'm not surprised by this at all