Minecraft v1.16.5
Forge v36.2.4
Trofers v2.3.0
Quark r2.4-316

When Quark is installed, mobs with variants use quark's shiny texture variants of those mobs. Is there a way to avoid this? Not sure which mod adds the villager iron golem texture though.

Ah, yep, I got the normal skins working by using a datapack and an UUID from a normal variant. And added all the quark variants at the same time. :) I might publish the datapack for it.

For the pig:
"nbt": "{UUID: [I; -1883173249, -554614415, -1774000146, 1551098959]}"

This is semi-intentional, although I should probably make it so entities on trophies don't have these textures by default.
Quark uses the entity UUID to randomly determine the entity texture. Entities on trophies have a UUID of 0 when their nbt doesn't contain one, which always results in a 'shiny' texture. I'm not entirely sure how UUID's are represented in snbt, but using a non-zero UUID should give you a normal variant in most cases.

In the latest update entities will use a non-zero uuid if their nbt doesn't contain one. I've kept the special quark variants of the cow and iron golem since I like those the most :p