A little of both, some in one direction or the other. For me it comes quite naturally, but I was raised myself in an environment conducive to parenting gently and naturally. I had parents, grandparents around, aunts and uncles, just a very open and supportive, loving, creative family. There were things, of course, that I disagreed with and don't perpetuate onto my own children, but they are minor things in the big picture, and mostly I think I went into parenting with a good toolkit from my own.
If you intend to go against what was done to you in a big way, I think it does have to be more learned, at least learned consciously moreso than just from what you learned while living it with your parents.
I don't think most things, that aren't purely biological functions, are 100% innate. We need some kind of observable behavior before we know to do it. Most mammals seem to function that way. I used to raise orphan livestock animals for local farms when I was a teenager. They'd survive their young life and thrive, physically, but a funny thing happened when they had their own offspring: many just didn't know how to be mothers. Most were put with other livestock at a few months of age, once they no longer needed round-the-clock care from me, but not observing that mothering behavior of their own species at the earliest ages left them clueless. Their milk would come in, they'd give birth normally, but they just had no clue what to do with a baby. At best some could be taught how to be good moms with careful guidance, at worse they rejected the baby or even turned on it. This seems to be what my generation is going through. Having to unlearn things our generation's parents did, and re-learn a different way of life and of interacting with children on the most basic of levels.