How patriarchal are middle east countries compared to the U.S. really?

Thinking about this today.

The Egyptian Women's Volleyball team dresses in a hijab to play volleyball to please men. The American women's volleyball team dresses in a sports bra and bikini bottom set to please men. In both countries, the women won't legally be punished if they don't, but they choose to.

https://www.bbc.com/news/magazine-37009324

In Egypt, women are directly told to be subservient and to do what they are told.

In America, women are indirectly socialized to be subservient and to do things they don't want to do "not to be rude" or not to offend people's feelings.

It's obvious that in countries like Iran and maybe Saudi Arabia were women don't don't have legal rights and are punished can't be compared.

But when you compare us to middle eastern countries like Egypt where women legally have equal rights the same way they have in the U.S., how less patriarchal is the U.S. really?