I do several things to avoid being buried in goblin clothes:
Most importantly, I have everything forbidden on death, and I don't unforbid goblin clothes without marking them for dumping at the same time.
Secondly, I don't allow clothes in my finished goods stockpiles.
It helps that I almost never make clothes for my dwarves anyway. But when I do, as I did in one fort where I was actually saving and trading goblin crap, I stick to pig tail cloth, which goblins never have. Then I just set up my stockpiles to assume that any leather or silk clothes are goblin crap.
I also set up special stockpiles for things to melt, near my smelters. They accept metal non-usable armor, metal arrows and blowdarts, metal weapons of types dwarves can't make (scourges, scimitars, etc), and metal finished goods of headwear type only (the iron masks goblins bring are actually finished goods/headwear, not armor).
When I have a battlefield to clear, I reclaim all the corpses and body parts from the stocks screen so they can go to the refuse piles to rot into bones. Once the bone sources have been hauled away, I reclaim all the remaining objects, then mark them all for dumping, then mark them all for melting; the melt designation is only accepted by the metal objects and automatically overrides the dump designation.
Normally I build a drawbridge-based trash crusher either just outside or just inside my fort's main gate, to minimize hauling time for all the narrow crap that's getting dumped. If it's outside, I disable the dump zone and enable one indoors when not clearing battlefields.