[R]eading a thread of comments from parents about “what I’d do if they did this to MY kid” is VERY VERY disturbing ...
Saying and reading those kinds of things gives your brain a bit of the experience of those things happening, without them actually happening, and that can be both personally cathartic and generally popular for the same reason. And it's easy to fall into the trap of coming to believe that you actually would want those things if the opportunity were presented to you, when the opportunity has not been presented to you.
There's a bit of selection bias, too. It's far less likely that someone is going to stand up and publicly say that they wouldn't want vengeance against a child murderer, because the general public has a hard time separating the notions of "not wanting to torture people" and "wanting a just and safe society." Human societies, to some degree, embrace violence. That's why prison rape is "funny." I would like to do better than that; I think that a just and safe society can be achieved without also embracing violence as a measure to accomplish it.
I'm also willing to bet that a significant portion of the people who are doing the “what I’d do if they did this to MY kid” thing are not parents. A different significant portion are doing it as a kind of virtue signalling.
Edit: Finally, imagine a scenario where Someone On The Internet says "I'd cut his dick off and shove it in his mouth." Okay, the court determines that the appropriate punishment is for the person to have his dick cut off and shoved in his mouth by that Someone On The Internet. Go ahead now, actually do it. I think the number of Someones On The Internet who would actually follow through with that is vanishingly small.