I don't know if there's a textile-specific equivalent, but mechanics have a marvelous thick glop they put on their hands before donning gloves. It's called GOOP. It's a chemical, not physical, barrier against oils, solvents, gas, etc. After work one unpeels the gloves, rinses the GOOP off, then washes hands as per normal.

If you can't find GOOP, there's also a class of soaps which have grit swirled into them. LAVA is the one most advertised on TV; there are scores of others. It's not much fun to wash with them, since they sandpaper off the top layer of skin. But if that's all the deeper the dye has seeped, LAVA would be your friend.