Certainly, Da’as Yehudis is a social principle; aka one of dignity. One woman (and a man, in a different context) must maintain her dignity at all times. In an all-female environment, one may maintain her dignity even when dressed differently then in the street. This applies to every single place and enviroment a woman is in.
Each situation has it’s daas yehudis. I understand there is a modesty which frum women have when swimming amoung themselves; this too would be daas yehudis.
One certainly loses dignity when being exposed in front of non-jews- unlike when around women. Hence, daas yehudis would forbid it. Forbidden, even in the Bahamas.
Beyond that, we have the dorasayah aspect of lifney iver. Lifney Iver does apply to a non-jew, as well. Hence, we have the multitude of issurim regarding causing a non-jew to worship avodah zara, to the point the beis yakov forbids business parntership with an akum; worrying that it will lead him to swear in the name of his god. Worry not, the Remah permits it based on the fact that non-jews are not prohibited from Shituf (aka christianity) – who leaves out the shaala of paganism.
We find a machlokes haposkim as far as if non-jews are obligated in hirhur relative to a woman who is forbidden to them. I presumably the lifney iver is contingent on that. Of course, the question continues of trey avrey d’nahar, which I wonder how to apply to modesty. Presumably trey avrey d’nahar always applies (aka creating issur and non merely facillitating it).
I would find this, therefore, to be forbidden (I didn’t see R’ Moshe, but I presume that his permission for a male lifeguard is based on tarud b’malachto, just like a doctor. I would be hesitant to apply this to a hairdresser; surely enough intelligent bais yakov girls become shaitel machers? In Israel, I have heard that charedi beaches often have male lifeguards, based on the fact that beach requires additional strength to pull a woman out of the water, and therefore they are mekel – even though they could easyily hirer female lifeguards)