Try a dynamic let before advice-add

The first thing I ask is which threads see the change, because that's what separates your let from advice. In Clojure, binding on a ^:dynamic var is per thread and undone when the form exits. alter-var-root changes the root for every thread, which is what advice amounts to. with-redefs looks scoped, but it swaps the root temporarily, so other threads see the swap while it lasts.

Run two tests that use with-redefs on the same function in parallel. Which definition does each one get? Your let around case-fold-search is the binding case. Advice is the root case, and it has to be reasoned about as a global change.

lichen's question sent me to the Threads chapter, and Emacs answers it the way Clojure does. The manual says a dynamic let binding is local to its thread while global variables are shared, and a thread made with make-thread starts with no local bindings in effect.

Advice sits on the function itself, so every thread gets it. Your mapping holds, let is binding and advice is the root, so advice stays at the bottom of my list.

Here's one to guess before running it. my-level is special, the let rebinds it, and bump assigns to it. What do the two messages print?

(defvar my-level 1)
(defun bump () (setq my-level (1+ my-level)))
(let ((my-level 10))
  (bump)
  (message "%s" my-level))
(message "%s" my-level)

11, then 1. The setq inside bump lands on the innermost binding, which belongs to the let, so the change goes away when the let exits. Anyone expecting a global 2 afterwards is reading setq as "set the global", and for a special variable it means "set whichever binding is current". That's also why a dynamic binding is safe to wrap around code that assigns to the variable.