I think this is the sort of thing that varies between states and even between counties.
We toured a part of our state that is a natural wetland, with serious canals and water management issues, and when someone mentioned cattails, all the natives swore up-and-down that they were protected, you weren't allowed to touch them, and all of us from out of town were like 'its a weed, nobody cares'. We concluded regulations were different.
Unfortunately, that probably doesn't answer your question very well.
However, if you want to grow them, not rip them out, the term you are looking for is 'noxious weed'. Those are the plants the government says you aren't allowed to grow. Try searching for your state/county and noxious weed listing.
I didn't see anything about cattails being a noxious weed anywhere, but I also am not up on all the various species and latin names to be sure. I imagine there are a number of things that may be colloquially called 'cattail' in different regions.