What is meant by "impedance sensitive device?" Why do some pedals care and others don't?

When we talk about "impedance sensitive" pedals, typically we are referring to very early, simple circuits like classic fuzzes and wahs (classic fuzzes would be fuzz-face, maestro, tone-bender, etc. 60s designs).
Often these used Germanium transistors (different effect than germanium diodes) and relied heavily on the interaction between the guitar's pickups, onboard electronics, and even the cable to create what has become "the sound" of these pedals. Silicon transistors were used too, and while they react a little differently, most of the interaction is similar electrically speaking.
The circuits themselves had relatively low input impedance compared to the existing "circuit" of the electric guitar and tube amplifier of the day. When added in, the effect clamped down on the top-end in a pleasant way when taken in the context of the fuzzed-out sound. Additionally, the interaction with the guitar's onboard volume control created an ability for the player to "roll back" the volume knob to create a sound more like a mild overdrive than an all-out fuzz. If you used a medium or long cable, the low-end would develop a pleasant little droop and there you go, the classic fuzz sound. Most of these circuits use specific capacitors to compensate for the clamped-down top, so the circuit uses tone-shaping components to compensate for the loss incurred due to the topology. This is why EUNA and any other active amplifier stage can affect them so strongly, because the loss is removed but the fuzz circuit has tone-shaping built-in outside of the tone knob.
As circuits evolved and got more complex, designers layered in other features and over time the circuits became a little less sensitive to these external forces. From a design standpoint, it's better across the board because the circuit basically does what it is supposed to do and sounds how it is supposed to sound more or less independently. Of course, different guitars will still sound different, but the wild variation in different circumstances has more or less been controlled. In general, designers don't have to use tone-shaping to compensate for loss any more, because we have other ways of preventing it, so they only have to design in the tone tweaks they are looking for. What's also true though, is that those wild variations allowed for players to make more unique combinations. THAT Fuzz-Face with THAT Tele sounds totally different from any other combination, etc.
These simpler circuits aren't more real or more legit than the later, more complex versions, but you can see how depending on your goals as a player these things could take up a lot of space in your tone journey. Players trying to get a classic, thick, late 60s/early 70s style fuzz sound have to travel this road of antique components and interactions between devices. If you aren't trying to get that sound you may be able to skirt some of the guidelines that sometimes seem like rules. I love a Big-Muff circuit, almost every variation I've heard, and I love the way they sound after EUNA. In general, the Muff is a good example of a circuit that still does the thing when used after another pedal. You don't have to be plugged right into it. I do use the EUNA loop for my favorite Tone-Bender type circuit made by R2R, because putting it after EUNA adds a good amount of "zip" that I don't prefer when I reach for that sound.  I have a Dusky Augustus after EUNA which I have tweaked to be very "zippy," that circuit could go either way and be happy.
As I usually say, "THE IDEA THAT COMPONENT SELECTION DOES NOT MATTER IS AS FOOLISH AS THE IDEA THAT COMPONENTS CAN BE MAGIC," meaning that while everything matters, some things matter only in a very small way, or only matter based on your own choices. The sheer number of components available to build circuits with is staggering, and almost all of them do something slightly different from one another, but not all of those aspects have a huge impact on the overall sound, and some of them have an impact on the sound only under certain circumstances.