Fortunately, your local hardware store probably carries several types of gloves. Chemical-resistant gloves are made with different kinds of rubber: natural, butyl, neoprene, nitrile and fluorocarbon (viton); or various kinds of plastic: polyvinyl chloride (PVC), polyvinyl alcohol and polyethylene. Nitrile gloves are very good for chlorinated solvents, alcohols, and oils, but are not particularly good around aromatic solvents, ketones, or acetates.
Here's an MSDS for Fiebing's dye: MSDS