Coconut milk, as it comes directly out of the coconut, is dairy-free and
presumably pareve. But many brands are "Americanized" which means that dairy
products have been added.

Most mayonnaise is also dairy-free and pareve, but I have seen dairy products
added to certain brands.

In both cases, check the labels. Food processing is an art, not a science,
and artists are always going to be a bit eccentric. [That's a joke, of
course. True, but a joke nonetheless.] For your further amusement, I offer my
web page: The Better Look Twice List of Supermarket Products That Appear To
Contain Milk -- But Don't!
http://ourworld.compuserve.com/homepages/stevecarper/notmilk.htm

Steve Carper

Steve Carper