This is a somewhat confusing subject depending on where you get your information. But it shouldn’t be, since this is not accepted in any area we have ever backpacked.
Some (tribal members), from time to time, have responded on social media stream bathing is acceptable. We have other tribal contacts that want this clarified that it is NOT acceptable .
We are talking about bathing. Not swimming.
What some locals/visitors/tourist may have done in the years past. Is totally not acceptable for visitors/tourists.
Our own tribal contacts strongly indicate that any stream bathing is NOT OK.
This following info normally applies in any backpacking or back country area. Supai isn’t some type of isolated anomaly. Generally it is Not OK to bath in the waters or use soap that enters the water (biodegradable or not).
In back country areas ( any non specific area) there is a general 200ft rule. Meaning no soap used within 200 ft of any water source. That applies to biodegradable or not. Many Eco-friendly backpackers feel the 200ft rule is even impossible to apply here in the Havasu Falls area.
Once you see the layout of the campground area. You will agree it would be nearly impossible to be 200ft from water. The canyon is too narrow.
Then even if you could manage to be in excess of 200ft away. This area sees a tremendous amount of traffic that is concentrated to a small piece of real estate. The sheer volume over time could damage the ecosystems.
Prepare for this before you visit the area. Do not promote stream bathing, shower bag showering, dumping soap or chemicals of any sort on the ground, etc. For body cleaning use some type of wipe (which you pack out), damp cloth wiping (no rinsing), or just plain do without for the few days you visit the area.