Catalyzes the transfer of L-fucose, from a guanosine diphosphate-beta-L-fucose, to the terminal galactose on both O- and N- linked glycans chains of cell surface glycoproteins and glycolipids and the resulting epitope regulates several processes such as cell-cell interaction including host-microbe interaction, cell surface expression and cell proliferation (PubMed:12692541, PubMed:7876235, PubMed:8018146). Preferentially fucosylates gangliosides GA1 and GM1 in the antrum, cecum and colon and in the female reproductive organs (By similarity). Fucosylated host glycoproteins or glycolipids mediate interaction with intestinal microbiota influencing its composition (PubMed:21625510, PubMed:22068912, PubMed:24733310). Creates a soluble precursor oligosaccharide FuC-alpha ((1,2)Galbeta-) called the H antigen which is an essential substrate for the final step in the soluble ABO blood group antigen synthesis pathway (PubMed:7876235). {ECO:0000250|UniProtKB:Q9JL27, ECO:0000269|PubMed:12692541, ECO:0000269|PubMed:21625510, ECO:0000269|PubMed:22068912, ECO:0000269|PubMed:24733310, ECO:0000269|PubMed:7876235, ECO:0000269|PubMed:8018146}. This is the function of Ensembl gene identifier ENSG00000176920 (FUT2, fucosyltransferase 2 (H blood group)).