IMHO what is innate is a person's capacity for empathy (the ability to understand that others have different feelings and to temporarily take their perspective for the purpose of understanding).

Empathy -- is a type of intelligence
Sympathy -- is an emotion
Compassion -- is a behavior (based on an emotion)

Whether a person actually expresses the empathy they have capacity for depends on things like whether or not they've been the victim of abuse. For example, the character Scrooge is what I'd call a person with large capacity for empathy but had no sympathy (the sharing of feelings with others) and thus acted without compassion. He lacked empathy for some reason, in some versions due to childhood abuse (never read the actual Dickens version so idk). The ghosts that visited him showed him why he should have empathy and because he had the capacity to, he changed.

I don't believe that every human has the same biological capacity for empathy. As a silly example, I don't think that the former pres. of the U.S. could possibly become a compassionate person due to being visited by the ghosts of Christmas past/present/future.

This concept of capacity applies elsewhere too, for example, my brain has a certain biological capacity to understand mathematics, but due to lack of motivation and interest, I am not likely expressing my full potential mathematical prowess.

Note that I'm using kind of reversed definitions of sympathy and empathy vs some definitions I've seen online. My way makes more sense to me, since the word "sympathy" is used outside of psychology the way I use it.

https://en.wikipedia.org/wiki/Sympathetic_string