Coconut milk is not “fake” milk. Just because it has the word “milk” in it. Coconut milk is the liquid extracted when you grate the white part finely and then squeeze out the liquid. There are plenty of liquids that are used in place of real milk – Almond Milk, Soy Milk, Coconut Milk. When mixed into a recipe, “milk” doesn’t stand out. I am surprised that you don’t have a problem with parve “creamer”. Cream is dairy. It is used in many desserts!
Before making people think they are doing something wrong – please look into all the details and speak to people who know more about this topic then you.