Sulfur is great for all mites, many pest insects, and some skin infections while being quite nontoxic as an additive. I've used sulfur soap and I've put sulfur dust in my chinchilla dust bathe for fungus and pests. I have had the most horrible tropical rat mites (those things aren't tropical) from pest mice every year here. We just got done with the attempted pest mouse move in this year and mite explosion again. They can't live on anything but mice and european rats but they survive a long time without their preferred food and bite increasingly desperate so my gerbils would go into seizures. With the redistribution from the continuing pest mice it's pointless to chemically treat the pet rodents and often they'd become too anemic or react and die from the number of bites if eggs hatched in their contained area before the mites could die from biting the treated animals.
The best thing I found is predator mites. These harm nothing but critters near their own size and will eat all mites that feed on animals. They first were sold as a way to kill fungus gnats and fruit flies in horticulture and that's still the easiest way to find the preferred hyopsis species (there's a few others but what all they are effective against I don't know) and it spread to use around animals that can't have medications easily like reptiles. They are now a pretty standard way to handle snake mites without ivermectin or constant cleaning and all sorts of pests in natural dirt enclosures with plants and insect cleanup crews. Only downside is they'll also eat all your natural smaller soil dwelling cleanup crew in such setups so you have to restock the tiny stuff every time you use them. You just put a dish of damp dirt with mites on the wire or in most cages of mammal or reptile and the little white critters march out to eat whatever they find. They spread pretty well with moisture or natural materials like even just the amount of wood in our house but need a boost of home base soil containers spread around for large areas of more sterile, clean materials like plain metal, plastic, or well swept concrete cages and floors. Sometimes they show up odd places and while they don't prefer it unless tracking food they might crawl on you or the animals but they don't bite and they will promptly die when they are done eating your pests. It's a fair trade off to having pest critters crawling on you purposefully. The only ongoing population I have indoors (there's some natural population in my native soil) are in a fruit eating gecko tank and if the fruit fly population spikes the mites spike to eat all the eggs/larvae. Then they will sometimes appear for a day in the next door bathroom probably due to the moisture before they are gone again. I'd rather see the harmless little dots for a day periodically than set out fruit fly traps and spray constantly. They have become my solution for near everything since they were the only way to finally kill those rodent mites and they are utterly nontoxic. They'll kill what's on the animals, eat the fungus gnats from potted plants or sink drains, and go after fruit flies. They are expensive to replenish frequently if you keep getting reinfested without an established source of them but to boost them once a year for my pest mites is cheaper than all the herbals, DE, sulfur, and various cleaners plus the effort versus setting out containers of damp soil and waiting.