You seriously know people who would like to require western women to wear it here?
How about starting with the local chicks first? See how they respond to that new dress code...

Muslim women are not even ALLOWED to wear it in the Grand Mosque in Mecca during Hajj, during the holiest of holy times; that should be a clue as to how much of a requirement it is.

As to not getting naked in public, both sides need to suck it up a little bit.
Locals that are offended: You're in a gym. People sweat and get naked in the changing rooms. Nobody is stripping inches away from your face, so just turn away or leave if it bothers you THAT much.

Expats who get naked: Understand that folks here are more uptight about the naked human body that you are, and cut them some slack. Go into the changing room to strip.

Saunas? If it bothers you to see naked bodies in a sauna, you shouldn't go there. If you don't like to get naked yourself, then fine, wear your undies or a swimsuit. But your body is meant to be naked in a sauna.

"If you're looking for sympathy, you'll find it between sh*t and syphilis in the dictionary."
- David Sedaris