Mushroom Biomes don't actively stop mob spawns. What happens is, every biome has a list of mobs that will spawn in it. By default, this list includes stuff like skeletons, creepers, zombies, most animals, etc... Mushroom Biome, however, has a list that consists of JUST Mooshrooms, so other mobs don't normally spawn within the biome. Soul Cages, however, aren't using the biome's passive spawning mechanic. They're manually making specific mobs appear in the world. Same reason why Magnum Torches don't interfere with spawners of any kind.
