I also think that purity (and impurity too) is complicated in Touhou cuz these words are not used in a very restricted manner. So I'm gonna try to help by focusing only on the Lunarians only here :
Whenever impurity has been mentioned, it's always been in relation to life and death.
There is actually also another suspicious brand(?) of impurity that the Lunarians are clearly not afraid of and is probably less related to life and death but probably more of it being impure as it's from earth : to illustrate, we have the Lunarian space probe from LoLK, which was virtually invisible to Youkai (who couldn't do anything about it) because the Youkai were too impure ; and we have the fact that Celestial flesh (actual pure beings) is toxic to Youkai and even have an uncomfortable presence to them ; and the fact that the Ultramarine orb's purification effect would instagib native gods such as Suwako ; and small speculation here but the possibility that the Youkai's defeat in the Lunar War, aside from technological inferiority, could have anything to do with their impurity imo.
1/All in all, the main takeaway here is the fact that basically impure beings are unarguably inferior to pure ones, and anything from the earth's make is impure (They even have shorter lifespans, inferior technology, probably dumber and stinkier too)
As for the moonies, since we've already seen the Watatsukis and EVEN Sagume personally go down to Earth despite it being rife with impurity (eww), I personally think the average unnamed Lunarian's distaste for impurity is more rooted in arrogance and ideology rather than in-universe lore understanding of it being bad for their health (not everyone should be on Sagume and Eirin's intellectual level anyway) : I think that aside from what WhitheringFlowerCrown said about Kaguya taking the hourai elixir, there shouldn't be a practical reason to ban Kaguya : it disconnects her from life and death anyway, so why ban her for impurity related pragmatic reasons ? It's gotta be ideological : she's basically failed the Lunarian ideological purity test by thinking like one of the stinky impure earthling, as in, taking the elixir cuz of mortality while she shouldn't even be afraid of that as a Lunarian.
2/So basically the average Lunarian's attitude towards impurity is that of a complete ideological rejection
As for the good old kegare, or the impurity of life and death that the Lunarians just can't handle, while I agree that it's probably still worth it to take Shinto Cosmology (rather than Buddhism) into consideration since Touhou lore uses traditional Japanese folklore, beliefs and religion as a backdrop anyway, I think it can be safely ignored since most of its relevant concepts are not really in use in Touhou : as far as this series goes, I think it's alright to simplify it as impurity from life and death.
But at any rate, when it comes to the difference between the moon and the earth in touhou, whenever we have something moon and purity related, it's generally about things staying the same : to illustrate, we have the moon's udonge tree for which blooming will serve to signal impurity so it's safe to assume they generally don't do that (cuz no impurity on the moon) ; and we also had Eientei be pretty much unchanging too before and during IN ; while in LoLK, the Entire capital was frozen in time to prevent impurity. Meanwhile, on Earth / Gensokyo we have Yukari's attitude in one of Marisa's LoLK ending where she's like "Gensokyo can change" (plus another FS chapter to that effect) ; and I also vaguely remember a Mamizou - Kokoro conversation where Mamizou tells Kokoro something that basically "life is about change" (although I can't find that conversation in the wiki ?? Srsly I remember something like that) ; and finally there's also Reisen, who changed from being a moon rabbit to a earth one during her stay in our stinky world : Thematically speaking, in Touhou the moon is always about eternity and the unchanging, while the earth is about change and growth.
3/Considering all that, I'd say that a pretty correct babyfied oversimplification is to say that impurity in touhou (the variety that Lunarians can't handle) is what allows change that lead you closer to death.