The point people are trying to make here is that if you do make two versions of the game, and you make them fully gameplay identical, one of the following two things is going to happen, and there will be absolutely no way to avoid it:
Scenario 1:
The "Touhou" version of the game released only through limited channels will be exactly what we expect, while the "non-Touhou" version of the game will actually just be a Touhou game with the serial numbers filed off. Now, granted, this is not an unheard of thing to happen in doujin fangames in general, there are a very large number of Touhou fangames which are essentially "fan remake of X commercial game but we've changed everything to Touhou references." Some of these do diverge from their source material a fair bit - Labyrinth of Touhou is clearly inspired by Etrian Odyssey, but actually plays much differently in practice, even once you get past the difference in dungeon perspective. Puppet Dance Performance is clearly inspired by Pokemon but has some subtle, yet important, mechanical differences from the game it's referencing, and has its own unique maps and such. For an example of the other way, Fushigi no Gensokyo, Touhou Soccer Moushuuden, or East Chemblem are all solid examples of Touhou fangames that are largely indistinguishable from the games they're based on in actual gameplay (Mystery Dungeon, Captain Tsubasa, and Fire Emblem, respectively). East Chemblem's plot even largely hits most of the same notes as the canon Fire Emblem: Shadow Dragon plot; it has unique maps and layouts, but the actual plot is mostly lifted from the canon game, only Marth is cosplaying as an adorable catgirl. Honestly, I don't exactly see why this sword can't cut both ways, and I don't think it's as much of a potential problem as some others in this thread seem to. (That said, it would possibly be very wise to still give ZUN/TSA a credit for the inspiration if you go this route, even if you end up making just one, non-Touhou version. Something as simple as a nod in the Special Thanks section of the credits, although I'd probably ask for permission before doing it. Better safe than sorry.)
Scenario 2:
The "non-Touhou" version of the game will be its own thing with no real association with Touhou, and the "Touhou" version of the game won't play anything like the fandom would expect at all, because you'd be slapping Touhou skins on characters who don't have Touhou skillsets. This is definitely the scenario where I feel it would be better to simply forgo making the "Touhou version" at all, because it wouldn't get the feel right.
I don't really see any middle ground between these possibilities so long as both versions of the game would have identical gameplay.