st. Nicodemus' quote goes even further I think,
Heracleides has also noted in the Lausaikon about Iouvinos, the famous bishop of Askalon, that on a very hot day near the Pelousion mountain he washed with a little water his hands and feet and laid out a camel skin to rest a little in the shade. This was done in the presence of his most holy mother, who directly began to reproach him. "Oh son," she said, "you are most daring to flatter you body with such care and at such a young age. The more you fuss over it the more it becomes agitated like a serpent against you, seeking to harm you. I am already sixty years old, and I have not yet washed my face and feet in such a way, except for my hands. Even though I suffered certain illnesses and the doctors advised me to take advantage of the therapeutic baths and other cures for the body, I have never entrusted in my body nor have I allowed myself to flatter it in any way, knowing full well the enmity that exists between it and the soul.
Is it really Orthodox teaching that such a hard line of enmity exists between body and soul? That such dualism exists between the soul and the body, that merely washing one's feet gives rise to some "evil inclination" within us?
For this reason, my son, I have even refused to recline in a soft bed to sleep"
Nicodemus continues later:
You have already heard above from the holy nun and mother of Iouvinos how harmful even simple bathing can be, especially to the young. In the act of bathing the sense of touch is certainly sorely tested and tempted. As we read in the sayings of the Fathers there were many ascetic fathers who hesitated even at the crossing of rivers, not only because they were ashamed to bathe their bodies but also because they did not even want to uncover their legs. These holy men were often in a flash transported across the river by an angel of God. St Diadochos, bishop of Photiki, has written that the avoidance of baths is a manly achievement. "It is a manly and prudent thing to avoid baths. This way our bodies are not effeminated by that pleasurable flow of water over them, nor do we come to a remembrance of that shameful nakedness of Adam, so that we too seek to cover the shame with the leaves of a second excuse. Those who desire to keep their bodies spiritually pure are esepecially required to be united with the beauty of prudence and chastity." Of course, it is understood and acceptable that occasionally one must bathe out of necessity for the sake of health and the requirements of an illness.
So bathing makes one homosexual? (or at least effeminate?) What kind of logic and theology is this? It's more "manly" to not bathe? Why on earth would celibate monks even worry about being more "manly"?
I'm fully aware of HOW this concept became entrenched within Christian thought, in both East and West. (it basically began, as others have posted as an anti-Roman idea, I'm fully aware of the history)...that doesn't make it "correct" though. Just because I can see and understand how and where the idea came from, doesn't mean I agree with it. I also see and understand, from an historical POV how the Papacy developed in the West, that doesn't make me a Catholic though.

I don't think what St. Nicodemus is saying here is carved in stone; I suspect that at the time he was writing, many monks were indeed bathing regularly, so he reacted to what he felt was undue luxury. Similarly, he strongly rails against bishops and priests wearing fancy clothing, and we see today how much his advice has been heeded!
I don't think it's carved in stone either, however....as you pointed out here:
In fact, St. Nicodemus seems less strict on this matter than some of his sources; the nun he quotes, for instance, seems to disapprove of bathing for even medicinal purposes, while St. Nicodemus thinks that is acceptable.
.....he was not the first, nor the last, to put forth this idea. It's not so much the individual I disagree with, but the concept itself, from a theological POV. I don't hold St. Nicodemus "responsible" for this belief, as you rightly pointed out, others before him said the same things, and in some cases were much more strict. But the idea...where did the idea come from? I realize it came from in many ways, historical circumstances, but in the end it is heralded as a theological idea. And the theology that underlies it is what I question. True, initially monks rebelled against the excesses of the Roman bathes. But that is not what St. Nicodemus, or pretty much any other ascetic father of the Church has taught for a 1000 years. St. Nicodemus is teaching it as a theological concept that bathing is bad because it awakens some ever present enmity between flesh and soul, body and spirit....the sense of touch, while he doesn't say outright that it is evil, (which would be blatantly gnostic) is at least so much a part of the the fallen order, that merely jumping in a cold stream for bath, would give rise to all sorts of temptations. So it is true he's not being gnostic, however it does sound very, anti-flesh to me. Almost as if he's saying it is beyond help, at least in this world. Of course anyone can interpret this any way one wishes, and I'm certainly no saint and have no special connection with God. These are just my impressions and opinions, and they certainly could be wrong.
Thank you for posting the full quote though, it has been very helpful.