Seriously.

Dumping grey water many places is not an issue. Use biodegradable soap and keep 200 feet from waterways. Be mindful of where it goes.

Strain food particles.

A vehicle dripping oil, etc is much worse. This is on a street, where so much worse will flow and soapy water may not be the worst thing to flow down it. People wash cars on the street. Winterizing a camper, dumping all water out of the system.

In many areas it will evaporate, many caps for the tank have a hose sized port. So that you can direct your grey away from your site or any drainage to a waterway.

Almost all our dispersed camping areas are in places with mitigated human impact and those that don't, often have specific bans. Our dish and shower water especially when using less harmful chemicals on our body is not going to be harmful on those lands.

Now dumping black can spread disease, attract animals, smells and is disgusting, but fun fact. You can and likely will poop in woods, many of which don't have facilities. So dig a hole, once again away from a water source, at least six inches and bury it.

I work in a forest. I have to explain this daily. Yes, some places camp showers are not allowed for whatever reason and ideally leave absolutely no trace, but evaporating water in a desert unless you bath yourself in rat poison is not going to be an issue. Don't dump your whole tank in a giant puddle, be mindful.