Head Coverings

Sa
In my faith, women cover their heads with a scarf or veil and I am very comfortable with this. However, my Protestant family and even my Roman Catholic family are very uncomfortable with it. 
It has nothing to do with "shaming" or being "inferior". Covering our heads is the mark of authority for a woman in Orthodoxy. I would love to wear it in public but I feel like this may cause unnecessary disruption to the social atmosphere here in the Bible Belt. 
How would y'all feel if you saw a Christian woman with a veil in public? How do you feel about women wearing a veil in church? And of course there's the question, would you automatically assume that a woman wearing a veil is Muslim?