I think you're ok on dishwater and washing machine water with most detergents.
I know it's legal in most inland waters for me to run my sink drains on my boat straight into the water. It is not legal to run the water from my toilet into any waters [fresh or salt] within 3 miles of the U.S. coast unless its's been treated in an approved treatment system and sometimes not even then. For boats and RVs, grey water is sinks. black is toilet.
What's your situation? We're in the country and the washing machine has drained into the yard for 50 years with no ill effects. It doesn't drain straight into the garden but iy's not too far away.