This path is already blocked by the collider at B, so we don’t need to control for anything. Many statisticians would control for B or C, thinking there is no harm in doing so as long as they occur before the treatment. A leading statistician even recently wrote, “To avoid conditioning on some observed covariates… is nonscientific ad hockery.” He is wrong; conditioning on B or C is a poor idea because it would open the noncausal path and therefore confound X and Y.
