I know you're not talking about slathering coconut oil itself onto your skin, but this article (even though it's just a blog post) has info on why coconut oil is problematic: https://rachaelpontillo.com/should-you-use-coconut-oil-for-skincare-maybe-not/
Given the explanation, I'd probably also avoid ingredients derived from coconut oil. Two of our children have oily skin, and they've tried a lot of products and found that washing gently with Cetaphil, and then patting the skin dry (not rubbing) works pretty well.