That is certainly an edgy post. While I understand your point of view, I myself have to make a distinction between a culture which thrives as unwritten law and a religiously based codex, such as the Sharia in Saudia Arabia, that is established as written and executed law.
We also don't know how much feminism has influenced Anna's decision. While feminists like to reap the benefits of existing gender segregations (male and female divisions in sports), they would protest against any unequal treatment in other areas of life that would put them at a, even debatable, disadvantage.