After cutting butternut squash, it's not uncommon to find a strange, scabby layer of gunk on the skin that briefly makes them warm and itchy, also known as "squash hands."
"Squash hands" is a type of contact dermatitis, a broad and annoying classification of skin allergies. Squash can cause it simply by brushing against exposed skin.
While the specific chemical compound inside squash that produces the rash is currently unknown, it seems to be linked to the Cucurbitaceae plant family.
Besides the obvious solution of avoiding the ingredient entirely, wearing food-grade gloves can protect your hands from the stinging squash. You can also buy it in pre-cut cubes.
If you find yourself with "squash hands," apply moisturizer, or a steroid cream if it's especially intense. Your hands should be back to normal in a half hour or so.