Catalyzes the transfer of sulfate to beta-1,3-linked galactose residues in O-linked glycoproteins. Good substrates include asialofetuin, Gal-beta-1,3-GalNAc and Gal-beta-1,3 (GlcNAc-beta-1,6)GalNAc (By similarity). Protein modification; carbohydrate sulfation. Belongs to the galactose-3-O-sulfotransferase family.