There is no real definition of "Clean" Beauty. Every business have created their own definitions of what ingredients aren't allowed. However, parabens seem to be consistently one of the "bad" ingredients. I don't think there is enough information to really make that conclusion, but you get enough people believing it, and cosmetics companies replace them just to be able to say they don't have them even though what they replaced them with might also be suspect as far as safety goes.
Parabens are very good preservatives that have been in use for years. There are other preservatives available, so there's no reason for a product to go bad so quickly unless they are using a preservative that isn't as good.
A completely Organic product I would espect would go bad quicker since the preservatives available that would be considered Organic are probably not that effective.