Peeled carrots are sweating, are they safe to eat?

I'm unclear what you mean by your term. Anything will form condensation on it if taken from a cold refrig to warm air and left out for a bit. However, if there's a slime on it from being left "unfresh" too long, then it should be tossed out. Antique veggies don't cut it.

My preference with carrots is to very lightly steam them as I read that it allows your body to digest the available nutrition better.