Catalyzes the transfer of a sulfate group to position 3 of non-reducing beta-galactosyl residues in glycerolipids and sphingolipids, therefore participates in the biosynthesis of sulfoglycolipids (PubMed:9030544, PubMed:8830034). Catalyzes the synthesis of galactosylceramide sulfate (sulfatide), a major lipid component of the myelin sheath and of monogalactosylalkylacylglycerol sulfate (seminolipid), present in spermatocytes (PubMed:8830034). Seems to prefer beta-glycosides at the non-reducing termini of sugar chains attached to a lipid moiety (PubMed:8830034). Also acts on lactosylceramide, galactosyl 1-alkyl-2-sn-glycerol and galactosyl diacylglycerol (in vitro) (PubMed:8830034). 3'-phosphoadenylyl sulfate + a beta-D-galactosyl-(1<->1')-N-acylsphing-4-enine = adenosine 3',5'-bisphosphate + H(+) + N-acyl-1-beta-D-(3-O-sulfo)-galactosyl-sphing-4-enine 3'-phosphoadenylyl sulfate + a 1-O-alkyl-2-acyl-3-O-(beta-D-galactosyl)-sn-glycerol = a 1-O-alkyl-2-acyl-3-(beta-D-3-sulfogalactosyl)-sn-glycerol + adenosine 3',5'-bisphosphate + H(+) 3'-phosphoadenylyl sulfate + beta-D-Gal-(1<->1')-Cer = 1-(3-O-sulfo-beta-D-galactosyl)-ceramide + adenosine 3',5'-bisphosphate + H(+) 3'-phosphoadenylyl sulfate + a 1,2-diacyl-3-O-(beta-D-galactosyl)-sn-glycerol = 1,2-diacyl-3-(3-O-sulfo-beta-D-galactosyl)-sn-glycerol + adenosine 3',5'-bisphosphate + H(+) 3'-phosphoadenylyl sulfate + a beta-D-Gal-(1->4)-beta-D-Glc-(1<->1)-Cer(d18:1(4E)) = adenosine 3',5'-bisphosphate + beta-D-3-sulfogalactosyl-(1->4)-beta-D-glucosyl-(1<->1')-N-acylsphing-4-enine + H(+) Lipid metabolism; sphingolipid metabolism. Expressed in kidney proximal tubule, gastric mucosa and adenocarcinoma (PubMed:9030544, PubMed:10785389). Highly expressed in renal cell carcinoma cell lines (PubMed:9030544, PubMed:8830034). Belongs to the galactose-3-O-sulfotransferase family.