I'm completely unconvinced. Maybe if you're talking about a crude caricature of science, about capitalism (not science) and greed (not science) objectifying nature, okay, I sorta see that. The Christian idea of the dominion of Man over the natural world, followed by the industrial revolution's demonstration of the power of machinery did, one could argue, lead to a very exploitative and destructive relationship of us to nature (and to ourselves, in some cases).
But if you listen to the enthusiasm and wonder expressed by Carl Sagan or Neil deGrasse Tyson, if you listen to the deep appreciation for, wonder at, and concern for nature expressed by David Attenborough or Jacques Cousteau, if you hear the giddy delight of Dianna Cowern ("Physics Girl") while demonstrating some complex physical phenomenon or the thorough concern for protecting nature of the otherwise stolid Kurzgesagt (Philipp Dettmer), you hear anything but "nature as worthy only of being enslaved", you hear not a "horrific mystery" but a "delightful mystery".
There is reason upon reason for how and why things work, and it troubles the scientifically literate hardly at all. It is only the conceit of the philosopher who imagines that we must have the last reason or the whole chain is pointless that renders the situation "zombified".
Maybe those who pay as little attention to science as they do to the natural world have a simplistic caricature of disenchanted, subjugated nature. But the overwhelming sentiment among basically everyone I know (and every popular figure I see) who actually cares about science these days ("these" stretches back forty-odd years--I'm not talking about Bertrand Russell's contemporaries here) is nothing like your characterization of either "ancient animists" or "modern quasi-animists". Through rigorous observation and careful study, we have discerned our place in the cosmos and our position in the tree of life, and we at once can both be scrupulously attentive to mechanistic detail, filled with child-like delight at understanding how things work, and deeply moved as if the subject of our study is an old friend.
So, anyway, no. I don't recognize this at all. If you do, the problem isn't that there's too much science, it's that there's too little, because people are clearly not appreciating the wonder of the universe we inhabit.