For same mean activity (or same concentration of pure salt added), the reduction in  for the case of dissociating salts will be twice as compared to that for the non-dissociating salts case.
But if is present in large amounts, its dissociation will decrease and the reduction factor for   will be lowered. This has implications in the case of detergency. In hard water, there are many salts present. Let us say is present in excess along with . Concentration of sodium ion and chloride ion remain almost constant on adding small amount of so the chemical potential of both sodium and chloride ions remain constant. Thus, dmNa term will disappear and the lowering in the interfacial tension reduces. Hence, it is difficult to wash clothes in hard water and thus water softening is needed to remove these impurity ions before using the detergent.