I suppose you could switch Probability & Statistics to "Just Enough Calculus" & Statistics to make it a less religious experience... but that also sort of defeats the "nobody really uses Calculus" mentality.
You also don't need a Jacobian, just the general concept of "How much does this change when we adjust this parameter in this direction".
I'm not saying it's easier without calculus. By virtue of being more knowledge, the ability to use calculus will always be easier than not having it, all else equal.
My argument is about opportunity cost. In my experience, people can get really good intuitions and tools around probability and statistics in the same time that they would otherwise learn the fine details around integrals and Jacobians -- and they'll find much more use for it.
I took 2 years of Probability and Statistics in Highschool in 1998-99 and 1999-00 at a school with 200 students. At the 4000 students school I taught at a few years ago we offered AP Probability and Statistics (had have been for at least 10 years, but probably much longer than that). In both situations, you could (and many did) take Stats without Calc.
Most times when people say "schools should teach X", many schools are (and have been) doing it (taxes, car maintenance, carpentry, gardening). Just maybe not your school ... or maybe nobody told you that it was a possibility at your school... Or maybe it's not at your school, but it is offered at another school in your district...
Or maybe it's just not offered at your school. Because there is an AP exam associated with Stats, it is fairly easy to get the class made as long as there are students that want to take the class and enough teacher slots to accommodate that. If a school is understaffed in the math department and class sizes are nearing 40, then you probably won't find a Stats class there.