Do You Have to Wear Hijab in Front of Non-Muslim Women?
Question

I have heard that a kaffir woman isforbidden to look at a muslim woman without her hijab. Is this applicable to my mother-in-inlaw who is an unbeliever?
Praise be to Allah.The scholars differed concerning the ruling on whether Muslim women can take off their Hijab in front of non-Muslim women , because they differed in their interpretation of the verse in Surah An-Nur (interpretation of the meaning):
“… and not to reveal their adornment except to their husbands… or their women…” [An-Nur 24:31]
There are three views concerning the Tafsir of this phrase:

That it means Muslim women;
That it means all women, Muslim and non-Muslim;
That it means Muslim women preferably but this is not binding.

The more correct view – and Allah knows best – is that it is permissible for a Muslim woman to appear (without Hijab) in front of a non-Muslim woman , unless she fears that the woman may describe her to her husband or to any other stranger (non-mahram man). In that case she has to keep her Hijab on in front of that woman. There is no difference between a non-Muslim woman and a corrupt Muslim woman in this case.
Among the evidence that it is permissible to take off Hijab in front of a non-Muslim woman is the Hadith of `Aishah (may Allah be pleased with her) in which she mentions that a Jewish woman came in to see her and said, “May Allah protect you from the torment of the grave…” (Narrated by Al-Bukhari, 1007; Muslim, 584).
Shaykh `Abd Al-`Aziz ibn Baz (may Allah have mercy on him) said:
“It is not obligatory to wear Hijab in front of them – non-Muslim women – because they are like all other women according to the more correct of the two scholarly views.” (Fatawa Al-Mar’ah Al-Muslimah, 2/582)
What the Muslim woman can uncover in front of a non-Muslim woman is the same as what she can uncover in front of her Mahrams, i.e., the places of adornment or the places of Wudu.
Shaykh Muhammad Salih ibn `Uthaymin said: “In front of her Mahrams she can uncover her face, head, neck, hands, forearms, feet and calves, and she should cover everything else.” (Fatawa Al-Mar’ah Al-Muslimah, 1/417)
And Allah knows best.