The authorities' argument is, that the mermaid fins violate the no-swim-fin policy. There are many public pools who forbid swim fins for safety reasons. Swim fins allow you to swim much faster than normal, which increases the risk of collisions and injuries with other swimmers.
However, when this policy was started, it seems nobody had ever thought that a woman could wear a mermaid costume in the pool. So, the legal question is rather: Does the mermaid fit the definition of swim fins or not?
Its more the inconvenience. You can't go fast enough to really hurt someone unless you get a head > to face type impact, which would hurt anyway. You are more likely to scuff or scrape people with the plastic edge of the fins.
Of course, this is all about someone forcing their preferences on others and using some "policy" as an excuse. Same thing with restricting grilles at beaches.
"About seven years ago, Conti had a brain tumor. She’d lost the use of her legs and had to relearn how to walk."
The mermaid tail might be considered a medical device, used to aid swimming for those who have certain medical conditions. Another tactic around the prohibition is that the mermaid tail is a single object. Frequently swim fins are used in pairs. So there is a clear difference between the two items.
There is also a distinction between a private policy and a law. As far as I know, she has violated no law in this case. It comes down to how the policy is written and if the the mermaid tail fits the definition of swim fins.
That how I understand it. It is up to the owners of the pool to allow or continue to restrict the use of the mermaid tail as a swim fin(s). Hopefully the issues can be resolved by the parties involved.