In some churches the custom is for women to cover their heads. If you attended that church would you go in bareheaded? Why?
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One could argue, on the basis of 1 Corinthians 11:5, that it should be the custom in all churches for women to cover their heads, “For if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered" But that, according to the verse only applies to “every woman that prayeth or prophesieth”
Just like churches and those who visit them choose to comply with or reject the custom similarly, it seems, dignitaries visiting foreign parts choose to comply with or reject the custom.