Human mutants are rare enough hereabouts is no general attitude on them. Case by case basis mostly. There are a couple unnamed Kenebac'ers with mild mutations - extra fingers, odd colored eyes, and there are a few people who are openly hostile, but they are similarly hostile to other outsiders as well, including Carnige.
So no burning at the stake, but low-grade discrimination may occur.
As for your cult, your call. Perhaps they are truly accepting, so even talking dogs could be admitted, or perhaps not.