Taxidermy has much more relation to the eye than the stranger. Hear me out
The stranger is associated strongly with impermanence of the self, disability, the uncanny, and the ostracized. The core of it centers around the unknown but it also has strong ties to change.
Breekon and Hope changing jobs to suit the needs of the fears, the not!Them changing those it takes in both form and memory, changing names, changing faces, flexible identity.
Taxidermy goes against this narrative. The main purpose for taxidermy from what I've gathered is education and preservation. Taking the time to care for a specimen in order to make it as lifelike as possible solely to keep it around for years after the taxidermists passing. Whether as a trophy or a relic the focus is on preserving the memory of what the creature was. It captures the individual in a permanent moment in time to have some element of it's story told for generations to come.
It's the preservation that doesn't make sense with the stranger. Even poorly done or inaccurate taxidermy still has the goal of preservation at it's core. Heck, even fur or skin rugs or animal-based clothing has some element of keeping context of the original. Real leather jacket, sheep wool hat from wherever, rug created from the kill of a previous hunting trip. For as much as these things are devoid of the original self, the lingering concepts of their creation are preserved to be taken again. Sound familiar?
Think back to the way Sebastian Adekoya describes books in MAG17. "There's plenty of scope for mutation and corruption between your mind and that of the listener, but that doesn't change the essence of what language is [...] There are written texts that have outlived the civilisations that created them. Imagine, thoughts hundreds, thousands of years old, preserved and ready to be taken again. Corrupted or translated perhaps, by a culture that does not understand them but still, ideas that have outlived by lifetimes the mind that first conceived them."
Taxidermy seems to fit that to a T. Even the portion regarding manipulation and false replication fits better for a connection to the eye more so than the stranger.
And what other things do we associate taxidermy with? The eyes. Ok yes they're glassy and uncanny but the feeling of being watched is something mentioned several times in regards to the taxidermy shop. MAG54: "hundreds of glassy, dead eyes starting at me from all directions [...] Every manner and type of dead skin surrounded me, frozen in uncanny stillness, as though they were trapped in a world where time has simply stopped [...] Their eyes had never been alive, and they all seemed to stare in my direction". Obviously that's written very much to focus on the stranger and I fully accept that the concepts surrounding taxedermy's uncanny results can incite discomfort. But the focus isn't the unknown. It's the fact that these creatures are removed from their original context to communicate some warped idea of what they used to be.
"I really don't want to be interrogating her where all those... a-animals can see us." -Archivist (I'm unsure why he's concerned here)
"What was stored here?" -Archivist
"Books, relics, but nothing since the skin." - Sarah Baldwin
"the oldest piece of taxidermy in the world" -Archivist (in reference to the gorilla skin)
The ties between the stranger and taxidermy are tangential. But the ties between the eye and taxidermy are direct. Besides it's not like the eye is above keeping physical reminders of people. Note the bones of Barnabas Bennett that "you can still find in [Elias's] office if you know where to look". And Jon's keeping of Jane Prentiss's ashes. And his keeping of his rib.
And we know the eye still has influence over non-literal depictions of eyes. MAG154: "James could watch us from any eye, even an illustration." - Eric Delano (deceased)
So with all this I believe that even though the stranger has power over taxidermy, the eye has a much stronger presence there than was previously insinuated. So much that I think given the right circumstances the eye could claim taxidermy from the stranger as a source of it's fear