Suppose a bacterial had a mutated repressor protein that could not bind to the lac operator. how, might this affect regulation of the operon

Transcription of the operon by RNA polymerase would not stop. This would, therefore, keep the genes in the operon activated without repression. β-galactosidase, lactose permease, and lactose transacetylase enzymes would still be produced by the bacteria even in a non-lactose medium.