I have never met a “left leaning Rabbi” that aren’t makpid about mixed swimming, tznius, etc. This is just right wing foolishness that doesnt understand the difference between halacha and how one practices halacha.
Anyway, why was my response about satmar deleted? I don’t think it was offensive at all. I’ll try rewording it, so here goes:
Satmar women do not learn tanach directly – they learn summaries in yiddish IIRC. So, they wouldn’t know a direct quote from Tanach.