James Frazier, writing in his classic book on the history of religion and magic, The Golden Bough (NY: Macmillan, 1951) notes that at Byblus, people were required to shave their head in annual mourning for Adonis. Women who refused had to serve as temple prostitutes. (pg. 384).
This may inform the thinking in Paul's confusing comments in 1 Corinthians 11. In Ephesus, where the many Gods were actively worshipped, something similar may have been required. In Paul's quest to balance Jewish ideals of propriety and local culture with the new faith - this may explain his comments.