It's usually better to say that they have "legal personality". They're not people, but like people, or charities, incorporated associations etc, they have an attribute that gives them legal existence a court will recognise.

What Citizens United established was that free speech applied to legal personality generally, not humans in particular. Folk forget that this includes organisations they like, as well as the many they don't. It's easy to dislike the situation (as I do), but trickier to explain how to define a way out of it.