For example, cross Naked in School with the magic school, Hogwarts.
There actually is an incomplete "Naked at Hogwarts" out there.
In some respects a clever author could probably weave the two timelines together fairly well.
Where the changes/backstory that Karen Wagner outlined for the NiS premise is actually the outcome of a bunch of witches(and possibly wizards--in the Wagner version men over 21 couldn't go naked in public) deciding they didn't want to wear clothes(or illusions of clothes) while out in public.
It just becomes a matter of why "the wizarding world" became so interested in nudity(and sexuality) to the point of "actively meddling in muggle affairs."
Keep in mind, timeline wise, Harry Potter runs from 1991 to 1998. Karen Wagner goes Naked in School, as a non-magical, around 2001. Logically if this came from the screwy magical world, that "would explain a lot" about The Program in general, but also imply the Magical World is (mostly) on board with the idea, meaning they probably have already implemented their own version before "the muggles do."
It just becomes a "how and why?" Problem for a writer, and really, the Alternate Universe aspects of it ultimately makes it a very different story to what it was based upon, and mostly in regards to "theory and understanding of magic" as it relates to the Rowlingverse. As it pretty much requires nudity and/or sexual activity either strengthening a person's magic in general, or strengthening certain types of magic that are found to be beneficial/desirable enough for many magicals to pursue it aggressively and openly(well, openly on their side of things).