I'm really surprised, I think this is the first time I've EVER heard of chickens who DON'T want to eat them!
That's interesting that they are nesting in dry conditions. They are usually attracted to moisture. It's possible they just decided to take refuge in the hay when they sensed dawn to bunk for the day because they are nocturnal. Are there any other moist places around the hay? A leaky gutter or downspout, mulch, compost pile, or old wood pile? They are also very attracted to light and will crawl towards outdoor lights and things.
Anyway, earwigs are not dangerous or destructive. They are simply part of Mother Nature's clean up crew and scavenge for dead insects and decomposing plant material. Most people don't like them and want them gone because they don't like the way they look.
But they're harmless so you really don't have to put any effort into doing anything with them if you don't want to.