Catalyzes the reversible interconversion of serine and glycine with the modified folate sulfopterin serving as the one-carbon carrier. Cannot use tetrahydrofolate (THF or H4PteGlu) as the pteridine substrate. Also exhibits a pteridine-independent aldolase activity toward beta-hydroxyamino acids, producing glycine and aldehydes, via a retro-aldol mechanism. Thus, is able to catalyze the cleavage of both allo-threonine and beta-phenylserine. 5,10-methylenetetrahydrosulfopterin + glycine + H2O = L-serine + tetrahydrosulfopterin Is completely inhibited by addition of NaCNBH(3) in vitro; this reagent is a known inhibitor of PLP enzymes, that reduces the internal aldimine of PLP to the catalytically inactive and stable secondary amine. Is also inhibited by L-cysteine, which forms a thiazolidine complex with the active site PLP. Amino-acid biosynthesis; glycine biosynthesis; glycine from L-serine: step 1/1. Homodimer. Belongs to the SHMT family.