Im looking to a Homebrew Wii to have multiple games to speedrun. Is it considered valid to run a homebrew Wii or does it depend on the community rules per game?

Always check with the rules/mods of any games/communities.

Usually modifications to a console that allow it to bypass things like region locking is fine, it’s only when the modifications give some kind of benefit that they aren’t allowed.

For games like OOT, as an example, using homebrew is fine as long as the version of the game you’re playing through it is the same version that was released in the Wii Shop. If you play on a version not released in the normal Wii Shop, then it would be banned. Again, this is just one example, but every game might treat it differently.