Catalyzes the initial reaction in O-linked oligosaccharide biosynthesis, the transfer of an N-acetyl-D-galactosamine residue to a serine or threonine residue on the protein receptor (PubMed:8690719, PubMed:9295285). Has a broad spectrum of substrates such as apomucin-, MUC5AC-, MUC1- and MUC2-derived peptides (PubMed:9295285).