Al-Shawkānī says in Fath al-Qadīr (4/22):

“The genitive expression ‘their women’ shows that the concession is confined to believing women.”

Al-Bayhaqī states in Al-Ādāb (p. 407, Lebanon ed.):

“As for the words ‘their women’, we have been informed that ʿUmar ibn al-Khaṭṭāb wrote to Abū ʿUbaydah ibn al-Jarrah: ‘Some women among the Muslims are entering the bathhouses accompanied by women from the People of the Book; forbid that.’”

In another version he wrote:

“It is not permissible for a woman who believes in Allah and the Last Day to have her private parts seen by anyone except women of her own religion.”

I say: The first report is recorded by al-Bayhaqī in his Sunan (7/95) through ʿĪsā ibn Yūnus: Hishām ibn al-Ghāzz ibn Rabīʿah al-Jarashī narrated to us from ʿUbādah ibn Nusayy al-Kindī, who said: “ʿUmar wrote …” and so on. Ibn Jarīr also transmitted it (18/95).

I add: Its transmitters are trustworthy, yet the chain is broken, for ʿUbādah did not meet ʿUmar—between them stands Nusayy, ʿUbādah’s father.

Saʿīd ibn Manṣūr related it in his Sunan, as cited in Tafsīr Ibn Kathīr (3/284), and al-Bayhaqī took it from him with the chain: Ismāʿīl ibn ʿAyyāsh → Hishām ibn al-Ghāzz → ʿUbādah ibn Nusayy → his father → al-Ḥārith ibn Qays, who said: “ʿUmar wrote …” This is the other narration.