Chickens sometimes make really weird decisions on what to eat.
I was coloring my hair a very dark color that I didn't want staining the shower, so we went outside and my helper sprayed the hose to rinse my hair while I leant over a ditch that's over our septic (where the port thingy is). It may not have been the most ecologically friendly decision, in hindsight I'm not sure how bad it was to do.
But the chickens were out ranging and they made a beeline for the ditch as soon as we walked away... we turned around and tried to shoo them off and they were madly digging, pecking, and
swallowing the stained dirt!

By the time we got them all rounded up and back in their pen several had made second trips back to the ditch. So most of my current chickens have whatever is in dark hair color inside of them
Another time, we were working on a DIY project on the back porch, and we had a "run" for the chick brooder on the porch as well where we could watch them play.
I leaned a big but thin sheet of styrofoam against the bars of the run and went in to get a drink and visit the bathroom. When I came back out I was shocked to see the chicks had all but demolished the sheet of styrofoam, and their crops were bulging. "Popcorn!"
(they were fine)
So while I wouldn't be concerned about chickens playing in wood ash, any kind of mixed material is worrying. There's little cause to believe they won't find something very inedible to be extremely tempting.
The scariest is any kind of metal. They like the way it shines compared to the dirt. Countless stories on here of chickens eating metal objects, some stay in without causing harm, some cause deadly obstructions, and some can slowly poison.
I work hard to keep metal, glass, and other detritus picked up out of their run whenever it shows up. It seems to rise from the earth in these parts (multiple properties). But I am certain they have consumed such things when I wasn't there to prevent it. So I have a certain despairing revilement for people who bury/burn refuse and leave the remnants to defile the land for generations. I once stepped on an absolutely wicked 6 inch long super sharp nail with a wide head, the only thing that saved my foot was it got driven into my boot on the first step and when I swung my foot forward the weight of the nail was dragging in the dirt and alerted me before I set my foot down again. If that had been a horse, or a lesser shod human, it would have been awful!