Since the Nintendo servers shut down, hacks have been the only way to play Wii games online - and this one is by far the easiest to use. Just change your DNS servers and you can play online again!
https://wiimmfi.de/patcher/dnspatch
There’s still a thriving Mario Kart Wii scene because of this! You can play Mario Kart online basically any time. I’d bet there are hundreds of players online right now (really brings home just how large the human population is…). Here are the current online stats: https://wiimmfi.de/stat?m=8