I am desperate to play the original Japanese N64 Animal Crossing/Animal Forest game.
Before I go and spend money on a cartridge and passport, does anyone know the Passport works with the Japanese N64 version of Animal Crossing?
I think it depends on the type of Passport you're buying.
As you alluded to in the question, older versions of the passport were not compatible with all games, and consequently there would be risk involved in purchasing one if you wanted to play only 1 or 2 specific games (like Animal Crossing/Animal Forest). They also usually involved navigating complex lists like this, which personally I would rather avoid if possible.
An alternative to using an older Passport was, as James' answer notes, using Region Modification, though region modding is admittedly more technically demanding than simply purchasing a N64 Passport.
However, the newest Passport Plus III appears to work with all games from all regions. As noted in section 1.2 of this N64 Passport Plus III guide:
Unlike earlier convertors and previous versions of the Passport, this version will play every game on the N64 from every region with no side-effects such as bordering or 'ghosting' (a second 'ghost' image appearing on-screen giving a blurred effect).
As such, if you wanted to be sure the game would work, I'd recommend just purchasing an N64 Passport III for its ease of use and broad compatibility across both the PAL and NTSC regions.
If you have an NTSC Console I suggest performing a Region Modification to the Console or Cartridge. Otherwise you could purchase the "Adapter Wonder" which is really an extension circuit board with a nice case that avoids the region notch compatibility issue.
My previous testing was flawed so I'm removing that answer.