Am I allowed to eat in a married woman’s kitchen if she does not cover her hair?
This depends on various factors. Firstly, do you know if she keeps the basic kosher standards that are not necessarily kept by all kosher consumers such as: Cholov Yisrael and Pas Yisrael, etc..? In other words, what is her official standards?
Is she knowledgeable and active in checking salads for bugs? Does she check eggs for blood spots? Does she understand that there are many hechsherim and not all of them are acceptable to Anash?
If it seems to you that her knowledge seems adequate to run a kosher kitchen to your liking, then we need to consider the second question: can you rely on her Yiras Shamayim due to the fact that she does not cover her hair?
This would depend on her upbringing. For example, if she is only starting to become frum the reason for not covering her hair might be because she knows that many Orthodox women do not cover their hair and she considers herself like one of them, (of course this is wrong, but it is her nisayon – challenge). If so, it could be acceptable to eat in her home if otherwise, her Yiras shamayim seems to be good in all other aspects.
If, however, she has had a frum upbringing and now does not cover her hair, then this is a negative reflection on her yiras shamayim. This is since there is no true justified reason she can have that she is not covering her hair.
Therefore, the matter would depend on your kosher standards and the specifics of some of the above-mentioned points to consider.
Sources:
ראה שו״ת מהרש״ם ד, קלח. פרי השדה ג, קפח – לענין אכילת משחיטת בעלה. נטע שורק יו״ד סד לענין נאמנות על הטבילה. לבו״מ קמא או״ח פא בסופו. מהר״ש ענגיל ו, כט. אום אני חומה א, מ.
(On a side note: there is an interesting discussion if one may divorce his wife if she does not cover her hair. In the past, it was a reason for divorce. However, Poskim say that nowadays where lack of tznius is rampant, particularly in the area of head covering, even among otherwise religious women, and it doesn’t necessarily indicate immorality (See Rosh Kesubos 7:9) one may be lenient in this regard. (See Divrei Malkiel 3:145. Yabia Omer 3: 21, 13. Yaskil Avdi 6: 77 and elsewhere). The Rebbe writes not to use force in this matter.)
See also here:
Halacha #224: Trusting a Mechalel Shabbos
Halacha #492: How Much Hair may a Married Woman Expose?
Halacha #335: Kiddush in the Presence of Women’s Hair
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