My personal minimal experience with parenting children (4 year old and 2 year old boys). My 4 year old is a polite, quiet, inquisitive, observant, good natured child. I thought it was due to my attentive, responsive, parenting.
Then I had the younger one. He literally came out screaming. He cried the whole hospital stay in overflow recovery where I had virtually no nursing support, no nursery to send him to, and no family to help as my husband stayed with our older boy, and it continued most of the first two years of his life. His response to anything is to scream. Happy, sad, frustrated, confused, excited, needs something, wants something, all of it means screaming. Like full on, for reals, scream. It's only now that he's finally in the language explosion and has more words to express himself that I'm getting a break from being screamed at constantly. But he can still pretty quickly devolve to screams. Some kids are just screamers and there's not much you can do.
Now, part of my situation is a healthy heap of post-partum depression. After months and months of being screamed at, shutting down is just my really unhealthy way of maintaining sanity, the alternative being to let the pressure in my head off in a fit of rage. I'm better now, but may always have a "talent" for shutting down when they scream that others probably won't understand. I'm not trying to make excuses for inattentive parents, but just be aware there may be more behind it. Sometimes, I just can't. For us, that generally means removing ourselves from a situation, but that's not always possible.
So, to answer your question about how to become deaf to blood curdling screams - if you're screamed at long enough to crush your soul several times over, you can tune it out, but I don't recommend that strategy.
I'm not sure the ages you're hearing screams from, but I also work with elementary kids and can tell you that their general volume is shouting. Especially if there are more than one of them. They don't quite have the understanding that other people are other people and they just talk louder and louder, because they want to make themselves heard and don't really hear other people.
Having also been in the unfortunate position of being around an actual emergency unfolding, you'll know when it's a situation that requires adult intervention. Those screams are different.
If it's really concerning, you can contact the park authorities or even the local police department. If they're not busy a good lecture about "crying wolf" can actually work wonders, or so my mom says.