Sun, Lunar, and Akeno never seem to be wearing panties. The one time we see one of them wearing clothing that would conflict with their legs' transformation (Lunar's study session that her father walked in on), we clearly see her shorts come flying off. Any other time they're clothed and have their legs transform into their tails... we don't see any underwear come off. Justified in how troublesome it'd be having to retrieve their underwear whenever there's an accident with water.
So there's the epic Les Yay between Sun and Akeno in the bath when they practice maintaining their mermaid form in the water. That's all well and good, and reaches it's resolution when Nagasumi realizes what they're actually doing. However, Mawari overheard them as well, and she never receives any explanation. In fact, Nagasumi encourages her incorrect interpretation so that she won't discover that Akeno and Sun are mermaids. However, this means for that the entire rest of the series, Mawari believes that Sun and Akeno had sex in the bath. One has to wonder exactly how this colors her perception of the two of them.