No, it is not suggested to use a regular shampoo to wash out a Relaxer. Because products like Relaxers increase your hair's alkalinity and change the PH balance. If the product is not washed with something that can clean the hair properly, your hair could get damaged and lead to hair breakage.  Regular shampoos do not contain the elements that are required for the job. On the other hand, Neutralizing Shampoos are formulated to wash away the harsh components of a Relaxer and bring back the normal acidic PH of your hair. So, you must not use a regular shampoo; instead, use a Neutralizing Shampoo to wash out a Relaxer.