Even when there's a list of what's in it, there are certain areas where they are allowed to not list them because of "trade secrets" or whatevs. Look at the ingredients for spices as an example. In skincare products, the fragrance is an example so it only says "parfume" or just fragrance, yet it's one of the areas for some of the worst offenders of ingredients.
It is hard to "vote with the wallet" when the chemicals are present everywhere and we hardly know where all it is present - maybe if there is a list of top N most-used/common most dangerous items to avoid - popcorn bags for example.