The new Water Dungeons cannot be turned off using the World Customization settings.

What I expected to happen was...
Changing "Temples" or "Dungeons" on the World Customization's Basic Settings screen to "No" would cause Water Dungeons to not be generated in the world. I was expecting to see the normal ocean terrain where the Water Dungeon was before.

What actually happened was...
The Water Dungeon still generated in the world.

How to reproduce:

1. Create a world and locate a Water Dungeon.
2. Write down your coordinates and exit the world.
3. Re-create the world (to get the same seed), but before creating, change the World Type to Customized and set both Temples and Dungeons to "No".
4. Create the new world and /tp to the coordinates you wrote down from Step 2.
5. The Water Dungeon will still be there.

Here were the settings I used:

Note: I took advantage of this other setting on the Basic Settings screen to help me find a Water Dungeon. The seed and location above will not produce a Water Dungeon if you do not also change the Biome setting to "Ocean".