It sounds like there's a solution in not discharging directly from the beach showers. I wonder if it might be feasible to collect that water somehow and use it as greywater elsewhere: watering plants, for instance.
Most people who use beach showers have come out of the ocean. Swimming seems like the primary point of transfer of sunscreen from body -> ocean, not the shower.
The article addresses that argument directly.
It varies by where you are on the island, and I don't mean this as an excuse for wastefulness, but Hawaii gets enough rain that it wouldn't be worth bothering with.