Once after handing a Jordanian taxi cab driver a bill worth $0.10 rather than a bill worth $10 as a tip for a day-long trip, I was accosted with the insult "Some people have two left hands."
In much of the world, only the left hand is used for cleansing after using the toilet. The right hand is used for eating, gestures, and greeting. Left-handed travelers may need to be careful to avoid gesturing or handling food with their dominant hand, lest they offend their more traditional hosts. Shaking hands or handing an item with the left hand is considered an insult in many predominantly Muslim countries.
There are special rules of restroom etiquette in most Muslim countries. You may not be expected to follow the Koran's exhortation to enter the toilet with your left foot, but it is a major foix pas (and possibly a violation of local law) to carry any Muslim religious object into the toilet with you.
Unless you are guiding a blind or disabled person or your child, you are expected not to speak, greet, or socialize with others in the facility.
Restroom facilities in Muslim countries are usually equipped with running water (a tube at arm's length) rather than toilet paper for personal cleaning. The tube is used to wash both the bottom and the index finger of the left hand (never the right) used to complete hygiene. There usually is not a seat over the toilet, but seats may be available in toilets provided for Western visitors.
When water is not available, toilet paper may be supplied, but may not. Observant Muslims have a habit of stepping out of the toilet with the right foot, and retrieving any items of possible religious symbolism only after they leave the facility.
Rules for observant Muslims are considerably more detailed than these, but this should be enough to keep you from offending local sensibilities.