I don't know, but since no one responded, I'm bumping your post so more people may see it.
It's very strange looking and I have to assume it is something fungal, because that's what weird growths usually turn out to be.
Looking at the picture closely, the clump on the right appears to be coming out of your potting mix, rather than directly from the plant. What kind of mix are you using?
Aloe like dry, very well drained conditions, and is usually grown in cactus mix. If that is some kind of fungus, it suggests that you are keeping the plant and the potting mix too moist.