The permethrin is toxic to cats at lower doses than what affects other mammals or birds. However, once it's dried in the coop and on the chickens, it's okay for the cats who aren't washing the birds or licking that coop!
My barn cats have been fine out there, no problems. They aren't at the...
Reinfestation happens too, thanks to those cute wild songbirds. It's an ongoing management story.
Ivermectin does work very well, and also stays in egg yolks very well. At least throw the eggs away for a week or ten days, to lower the amount in each egg.
Some individuals are allergic to it...