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. Optimum pH is 6-7. Protein modification; carbohydrate sulfation. Expressed mainly in placenta, thymus, testis, ovary, spinal cord, trachea and adrenal gland and at low levels in brain, lung, spleen, prostate, small intestine, colon, stomach thyroid and lymph node. Belongs to the galactose-3-O-sulfotransferase family.