A few questions, first of all are you playing on the newest version of the game (43.05) with the new armour/property mechanics? The fact it may not actually be skin but instead a glob like substance substitute may have meant that you've turned everyone essentially into rubber due to yield/tear rates (as to how much force has to be exerted before a material breaks), concept may remain much the same outside of that version, all the skin in the world may now have extreme consistency as to unforseen botch job consequences.
Most likely cause is that skin in itself on a corpse is a component for tanning because its a body part
[REACTION:TAN_A_HIDE]
[NAME:tan a hide]
[BUILDING:TANNER:CUSTOM_T]
[REAGENT:A:1:NONE:NONE:NONE:NONE][USE_BODY_COMPONENT][UNROTTEN]
[HAS_MATERIAL_REACTION_PRODUCT:TAN_MAT]
In the product, if you want to use the reagent's material itself, use NONE instead of a reaction product class (TAN_MAT in this example).
[PRODUCT:100:1:SKIN_TANNED:NONE:GET_MATERIAL_FROM_REAGENT:A:TAN_MAT]
[SKILL:TANNER]
[AUTOMATIC]
Changing it to a glob screws up this reaction because globs and 'body components' are completely different, skin is its own body part that can in theory be removed, and from what i can gather, leather bats give off spare body parts from 'shearing', in changing skin to a glob, the values have been moved around and leather bats can no longer function as before.
Though i don't have first hand experience with either mod, they seem to take different approaches, i would recommend ditching your leather mod or finding some way to turn skin into a blob then run a seperate reaction to make so much leather out of the amount generated instead of having it on the base animal.
Alternatively use a butchering method reaction that disembowels a creature entirely (as per first removing the skin with a slicing knife tool, then using a boning knife to get the bones out, then letting the butcher carefully take apart the animal using a carving knife into body parts to be turned into leather piece by piece)