There are innumerable kinds of mites in the world that are red colored, the very vast majority being free-living (i.e not ectoparasitic on animals). Free-living red mites mostly do not bite people, but, some do (when I was a kid there were what we called 'sidewalk mites' that would bite).
For what it's worth, CHICKEN mites come in three common types (and some uncommon types I will ignore here) - scaly leg mites, which you are not going to actually see themselves, just the raised lumpy ugly areas they cause on the birds leg scales; the northern fowl mite, which lives almost totally on the chicken (tho you may see a few on bedding or roosts or eggs, or crawling on *you*) and they're teeny tiny and dark grey-brown; and roost mites, which spend the day hiding under the roost or in other places in the coop and crawl onto the birds at night to feed, and are more red-colored.
Chickens can get (and give) mites to other kinds of birds; but not to people or other mammals or other creatures. And, the free-living nonparasitic mites (which, again, accounts for the vast majority of mites in the world) do not bother chickens.
So, if you are seeing mites IN YOUR COOP, they are probably Bad Characters; but if you are seeing mites anywhere else e.g. your compost pile, they are virtually certainly harmless to your chickens. (Though, wild birds passing thru can leave behind some of their parasitic mites that chickens can then pick up... but you will never SEE those mites til they become an infestation on your chickens)
Does that help any?
Pat
