Yes. Not only that but when the head of a certain Modern Orthodox American seminary in Israel (I don’t know if MO is the right word – what I mean is that most of the girls came from MO backgrounds, and the school itself was not Chareidi/Yeshivish)had her son ask Rav Shlom Zalman Auerbach, zatsal, if they should make the girls wear socks, his response was, “All b’nos Yisrael wear socks”.
I was very surprised since I always understood it to be a minhag hamakom issue (as per the Mishna Brurah), and since these girls were from MO backgrounds, I wouldn’t have thought they would be required to wear socks according to Halacha.
I have heard other things that seem to indicate that the Gedolim feel strongly about socks and may not differentiate based on the background the girl is coming from. But I don’t know. That’s why I said you should ask a Rabbi if you want to know what you should do.
It would seem to me that if you are struggling with tznius, you should start with things that are clear-cut halacha, but again, I’m not a Rabbi.