SLS, if you look up in chemical dictionnaries, is an irritant, and drying, especially in repeated use, and considering you wash your body, your hands and your hair on a regular basis, i confirm it is in my case. This one is no longer welcome at home.
Sodium lauryl sulfate is supposed to be less irritating and drying, and is accepted in "natural" products. I have my pros and cons for this one. It really depends on the other ingredients. If your bodywash contains other moisturising ingredients, it will probably be ok. If not, better not use it.
I tend to buy rather than make my own showergel, i try to avoid the lauryl version as much as i can, but sometimes the selection of real natural/organic products is limited, so i have to pick the most acceptable.