In 1994 I taught a summer ethics course, and at it a student came to class every day in a burka. The full head scarf. She was from Jordan and was a very knowledgeable Muslim. I didn't think anything about it at the time; that was what I expected of Muslims.
Later on in 1994, another Muslim student came to class from Iran. She had no head scarf. I asked her about it, and told her about the previous Muslim. She said "Muhammad commanded us to cover ourselves so as not to call attention to ourselves. Now if I were to go around in a burka, what would that do? Call attention to me. So for the reason Muhammad told us to weara burka, I don't wear one.
This reflects two different ways of applying the same passage of the Qu'ran. But not just the Qu'ran. What do Christians do about "Women should not speak in church" out of I Corinthians?