if so which ones/versions are allowed?

All runs must be done on either a GameCube, Wii, or any other console that has an official re-release of this game. This is due to this game having a very poor track record of emulating accurately across various different PCs.

Just to clarify on behalf of a few friends of mine thinking about getting into it; what's the current stance on using ISO Loader Homebrew on Wii hardware?
I'm under the impression they're not allowed either but is that just because the research into accuracy hasn't been looked into yet? And is it possible we may see that as an option in the future?

ISO Loaders are also banned for this game since there are some advantages with using an ISO Loader such as overall faster loading times compared to using an actual disc. We might revisit looking at unbanning ISO Loaders when this game is no longer easily available to obtain/purchase. But for now, used copies of this game are still around the $10 - $20 range.