Mooshrooms currently don't have a working loot table. When dumping the mooshrooms loot table you'll get loot table . It seems the loot table was not relocated with the split: Path. Changing the loot table with Loottweaker will either result in no changes being made or an error.

For "normal" animania cows the loot_table resource location is ResourceLocation("farm/" + Animania.MODID, "cow_prime") but for the Mooshroom it is ResourceLocation(Animania.MODID, "cow_mooshroom");. No "farm/" for the Mooshroom so it will not find it's loot table .json file.

Does this work for any other animals of animania? What is the exact log/error of loottweaker?