Numbers show that 73% of Iranians want a separation between state and religion.
The punishment for not wearing a hijab is largely financial, although there are new systems to report women not complying with hijab rules to the morality police.
While some countries enforce the mandatory wearing of traditional headwear, several European countries have banned it or are considering banning it in certain public areas.
Niloofar Hamedi and Elaheh Mohammad were released on Sunday temporarily after paying bail.
As she was flogged, Roya Heshmati chanted "in the name of woman, in the name of life, the clothes of slavery are torn..."
In recent months, plainclothes agents have been seen in metro stations in Tehran, enforcing hijab laws.
"The roaring river finds its way, even if it has to pass through hard and impenetrable rocks," wrote the doctor after she was fired.
Iranian students said that violence and intimidation by security forces have driven some students to suicidal ideation.
Broadcaster BFM TV and daily newspaper Le Parisien earlier cited police sources as saying the woman's behavior indicated a possible Islamist "terrorist" motivation.
Mohammedi, a campaigner for women's rights and against the death penalty, is currently serving a 12-year prison sentence