That's a limitation of the Morrowind game engine where alpha channels overlap.
Most modded clothing uses alpha channels, especially when the designer wants parts of the underlying body or other clothing to show (e.g. transparent parts of clothes, holes in clothing, etc). Invisibility is achieved by using alpha channel transparency over the entire player model, and similarly the water plane uses an alpha channel to allow you to see below/above the water surface. Viewing your player in 3rd person across overlapping alpha channels causes the layer closest to the camera to override, so in these cases the full transparency has precedence.
The only way to avoid it is to use clothing without alpha channels - in most cases that would be the stock clothing.