Unfortunately the answer is no for many of the chemicals of concern. These chemicals are designed to do a job, and they do it well. They are designed specifically NOT to wash out. The chemicals are used because they are intended to last for the life of the fabric, which can be very long.
For instance, a commonly used class of dyes called “fiber reactive” dyes chemically bind with the fiber molecules in order to remain color fast. (Fiber reactive dyes are not necessarily made from toxic chemicals.)
Think about it: would you be happy if your permanent press sheets suddenly got extremely wrinkled, or if your shirts lost color in the wash?