Releases galactose by hydrolysis of plant cell wall galactose-containing polysaccharides such as galacto-xyloglucan, pectic galactan and galactan (in vitro). Hydrolysis of terminal non-reducing beta-D-galactose residues in beta-D-galactosides. Optimum pH is 3.5. Belongs to the glycosyl hydrolase 35 family.