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No, it is obligatory according to the major schools of law in Islam, which the manority follow.
Here’s the section from Encyclopedia of Islamic law: a compendium of the views of the major schools by Laleh Bakhtiar (archive: https://archive.org/details/encyclopediaofis0000bakh/page/70/mode/2up )
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Does it make a difference that it’s under the section “Prescribed Prayers”? Because the New Testament has a similar rule written in it that women have to cover their heads while praying.
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