Governments regulated women's choice to wear or not wear coverings on their heads in 43 countries in 2012, according to a recent Pew research study.*
In some countries such as Saudi Arabia and Iran, governments require women to cover their heads in public. Some countries like France, however, forbid female teachers and students to wear headscarves or other conspicuous religious symbols in public schools.
While the reasons for this relationship are complex, one contributing factor may be that women face more employment discrimination in countries where there is stigmatization of women who wear scarves. For instance, in Turkey, women were prevented for many years from wearing headscarves in universities and public offices. While the ban was reversed last year, this educationally disadvantaged women who wanted to wear headscarves. Also, there is lingering employment prejudice against women who wear headscarves.
For a broader discussion of how restrictions on religious freedom impact business, including in Turkey, see my recent op-ed - Brian Grim.
* Overall, the wearing of any religious symbols, such as head coverings for women and facial hair for men or other religious objects such as crosses, is regulated by law or by some level of government in 54 countries as of 2012, the latest year for which Pew Research data are available.