So, United, you are a muslim woman, since you say you have been mistaken for a Christian Nun? Well, first that would depend on the order of nuns, they don't all have the same headcovering so I would hardly say that they look like they're wearing "hijab" unless you're using that word to mean anything a woman wears on her head. Secondly, the people who have mistaken you for a nun, may not know anything or much about nuns, EO, RC or Anglican (yes there are Anglican nuns).
As to *why* nuns wear certain styles of headcovering, for many western orders they are wearing what was the mode of widows clothing or very simple gowns from the time the order was founded. Thus older orders (Benedictines, Poor Clares etc) have habits that are drawn from many hundreds of years ago. More recent orders such as the Sisters of Charity, founded by Mother Elizabeth Seton, wore bonnets and clothing such as were worn in 1809 when the order was founded. Or it may be due to the country that the order was originally from, or if they are a contemplative order or a nursing order or teaching and so forth. Some are quite plain, others have been very elaborate with sort of wings or cornets or ruffles. (I have read for for some orders, the nuns hair was regularly cut very short/shaved so that there was no call to fuss with it.)
There are many factors that apply when people make clothing: climate, working conditions, what materials are available and such. Humanity is a richly complicated thing.
Next, You are incorrect that St. Mary the Virgin is *always* shown with her hair covered. Most of the time, yes, but for example, I had an icon of St. Mary showing Jesus in a mandorla in front of her and her hair was hanging as a maiden wore it. (In some cultures little girls and maidens wear their hair uncovered until marriage). This was an icon that I had purchased from a shop attached to ROCOR, so I hardly think that it was incorrect or unacceptable.
You say the passage is "plain". But perhaps it is not as plain as you would like to present. The whole business if being the "head" of someone. When it says "the head of the woman is the man" one question is "Which man?" "Any man?" "Her husband?" (What if she's single?) "Her father?" (what if he's dead?) And just what does "Because of the angels" mean? I have read that for the culture and the time, the covering of the head by an adult woman has as a purpose modesty, which St. Paul also writes about. So stating that for Christian women covering means "Male domination" is overly simplistic. Jewish women also wore some kind of covering and in Hassidic and Ultra-Orthodox groups today, married women will wear a hat or a wig to cover their own hair for modesty (it going with hair being a woman's "glory" but only for her husband, I'm told.)
Then, women wearing something on their heads was not just a "Catholic" or 'Orthodox" thing. There are cultural aspects to wearing hats/bonnets/veils/caps that crossed religious lines in Europe, the Middle East and the Americas. Colonial era American women wore a variety of caps and hats. Looking at the history of clothing from many lands can be quite interesting and information.
In Africa south of the Sahara, Asia, the Pacific Islands and Australia, the European patterns don't fit.
Then there's the question of 'hijab' for modesty meaning just covering the hair, or the face or wearing the burqa? I have read of too many cases where Muslim men have beaten or otherwise harmed muslim women for what the men thought was a breach of modesty. If it's not for male dominance, why are strange men taking it on themselves to upbraid and mistreat women?
Edited to complete a sentence. I sometimes think faster then I can type.