How is mixing (of sexes) forbidden, when the female Companions used to treat the wounded in wars, and a Muslim woman went to the market of the Jews, which was the cause of a war between the Messenger of Allah, peace and blessings be upon him, and the Jews of Medina?

The mere gathering of men and women in one place is not unlawful mixing. However, it becomes unlawful if it involves prohibited شرعية matters such as: khalwa (private seclusion) with a non-mahram woman, looking with lust, a woman's immodest display and lack of decorum, frivolous play, and physical contact. The fact that female companions (Sahabiyat) went to markets or participated in jihad did not necessitate their falling into unlawful mixing. Similarly, a woman treating a man medically when necessary is permissible with شرعية ضوابط (Islamic legal controls) and is not considered unlawful mixing.