Nope, not a problem as long as its design specifically for washing hunting clothes (doesnt contain any UV brightners or is scented) Just to let ya know, I wash my Scentblocker Dream Season suit in Scentlok detergent.

Keep in mind, It is only recommended to wash activated carbon suits only when needed (ie-covered in blood or mud) Only 2-3 washings per season is needed. Many washing will begin breaking down the activated carbon.