Ew...guess that means the dish is no longer vegetarian?

I understand completely! I've cooked with butternut squash without a problem for years but about a month ago the same thing happened to me. It took forever to get it all washed and rubbed off. It was like a thin pale orange film crinkling up my skin. It hasn't happened since but I researched it and here's what I learned: it more frequently happens from the pulp when trying to remove the seeds, and some say it comes from something released when you peel the squash with a potato peeler before baking; either wear gloves or wash your hands frequently; speed up separating the seeds from the pulp by soaking in water for 30 minutes so the seeds will start to separate from the pulp and float to the top. Hope this helps!

I used to be a savory cook in a bakery and I'd spend an hour just chopping up butternut squash. I always encountered this problem. Gloves will prevent it, but if you don't like wearing gloves while you work (I don't), try this. Once I was done, I'd wash my hands in hot (hot as you can stand) soapy water and scrub gently with a nail brush. This will remove most of the sticky squash juice if you're patient and gentle. Then put on some good moisturizing hand cream and let your hands rest about 5 min with it on, just to soak in. This usually worked quite well for my hands. I'd often have a small bit left even after all this, but it'd wear off after about an hour and wouldn't bother me in the same way. Good luck!

I guess it could be an allergic reaction, but both pumpkin and butternut squash contain a natural astringent - in fact, there are natural skin care products that contain their extract for that very purpose. So maybe your skin is simply especially sensitive to the drying effect of this compound. But I agree that your best bet for prevention is to wear rubber gloves - if you can get surgical ones (e.g., at a medical supplier) they're the thinnest and allow the most dexterity for doing things like peeling or chopping.

Super common. Wash gently. Maybe take an antihistamine? If it doesn't go away go to a doctor.

Next time wear gloves. I keep latex exam gloves around for chopping pepper and such.
Or cook your squash before you peel and chop it.

oh my sounds like you are allergic to some part of the squash! Some kind of contact dermatitis or something. Well, for future, be sure to wear latex gloves for sure.

As for what to do right now, totally not sure. I'd first wash well with gentle soap and water. Must be something you can apply to the skin to soothe, like cortisone cream? I would call the pharmacist. I'd ask them.

My mother had a similar reaction when she was in her garden fooling with the fig leaves and the pumpkin leaves. Burned like crazy. She put some ointment on it - I don't know what.