Modesty in toileting was exampled among Jews and Persians long before Muslims came along

Rembrandt etching of woman urinating

When he was gone out, his servants came; and when they saw that, behold, the doors of the parlour were locked, they said, Surely he covereth his feet in his summer chamber.

-- Judges 3:24 

And he came to the sheepcotes by the way, where was a cave; and Saul went in to cover his feet: and David and his men remained in the sides of the cave.

-- 1 Samuel 24:3

One seldom sees a Persian stop to pass water or step aside in response to a call of nature; so scrupulously do they avoid these and other unseemly actions.

-- Ammianus Marcellinus, Roman Antiquities 23.6.79

There remains even unto this day evidence of their moderate fare and of their working off by exercise what they eat: for even to the present time it is a breach of decorum for a Persian to spit or to blow his nose or to appear afflicted with flatulence; it is a breach of decorum also to be seen going apart either to make water or for anything else of that kind. And this would not be possible for them, if they did not lead an abstemious life and throw off the moisture by hard work, so that it passes off in some other way.

-- Xenophon, Cyropaedia, 1.2.16