From experience it depends - info Seven years old - on where and what beach you visit. Some allow bikini bathing others do not. Most of the locals swim fully clothed.
Recently there has been a move away from this for the richer folk who wear the more conservative Full body suit. This covers the the whole body from neck to ankles to wrist. These now appear to be approved on all Arab beaches as we have sold many to places like Egypt, Jordan, Saudi Arabia, and Iran.
Former belly dancer:
Only in private hotels that accept foreign tourist permit bikini or western style swim wear only in private access pool areas that is sequestered off from public display meaning indoor only or those that have gated security and tolerate or cater to western cultural.
In the past 10 years much has changed and expect the information about western wear to change again under Egypt's new leadership, ten years ago as a belly dancer the mid-driff area of the body was permitted to be exposed but no longer requires more Islamic modesty laws today! Only now with special government permission (fees for security guards) does even a belly dancer allowed to show her mid-section abdominal area bare if so again it's usually at a western style hotel with restricted and or limited access to the public as the location of most open international dance competitions are held.
Yes there are Islamic modesty protests and the need of both police sometimes soldier guards as the protests can be violent. Rule of thumb do as the locals follow modesty practices to avoid conflict. Last there 2009.