Johnson's Baby Oil

This product is pretty much pure mineral oil and fragrance. Not good for anyone's skin, let alone a baby!
That said, it's OK to take make-up off with PROVIDING you take it absolutely nowhere near your eyes. That way leads conjunctivitis as best, blindness at worst. Yes, we all know someone who's done precisely that for years. But my uncle's been smoking 40 untipped a day for 80 years - that still doesn't make smoking healthy!
Being mineral oil this will certainly emulsify heavy make-up and help you shift it. But because it's an oil product in an of itself, you do need to use a product which, in turn, can emulsify the oil and remove it from your skin. Mineral oil is not at all good for skin, and is highly comedogenic - ie likely to cause lots of spots and blackheads.
Having said all the above, however, most people are a lot better off keping this stuff well away from their faces - I certainly wouldn't allow it anywhere near any part of my anatomy!
The only ones who will benefit from this are those with allergies to all botanicals (natural products), of whom there are very few indeed.