Is a Muslim woman permitted to be in the bathhouse or reveal her face/head covering to a non-Muslim woman?

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The prevailing opinion is that a Muslim woman is not required to veil her face or refrain from entering a bathhouse with a non-Muslim woman (Dhimmiyah). This is based on the evidence that non-believing women, including Jewish women, used to enter the households of the wives of the Prophet, peace be upon him, and the Prophet did not command a veil be placed upon them. Furthermore, Aisha, may Allah be pleased with her, interacted with a Jewish woman who visited her, and Asma, may Allah be pleased with her, was permitted to maintain ties with her mother despite the mother's rejection of Islam. The legal reason (illah) for veiling between men and women is absent between Muslim women and non-Muslim women, similar to the ruling between a Muslim man and a non-Muslim man, meaning the restriction of veiling should not apply.