Dolphin is an emulator, community/dolphin-emu on Arch.
If you have real Wii motes: Dolphin uses its own drivers so do not install xwiimote or anything similar, do not use bluetooth GUI or anything, simply connect a bluetooth dongle and start the BT service via
sudo systemctl start bluetooth
if it isn't on already. Go to Controllers in dolphin-emu, set at least one Real Wiimote and check continuous scanning. On pressing 1+2 or the red sync button the controller should connect and vibrate.
All chinese BT dongles will likely not work properly, throwing various errors at you when you try to use them with Dolphin.
Note: The wii motes can glitch out - you will need to take out the batteries for a second to get them to connect again.
You need to add ISO directory with your game ISO files to do so go to Config > Paths > Add... and select the directory.
You may want to go to Graphics > Enhancements and set the resolution to auto and use some AA and/or Anisotropics Filtering.
You should also go to controllers and check that the GC/Wii controllers are configured(You can always reset them to default).
Dolphin-emu has an awesome feature called Netplay, allowing you to play the games with your friends over the internet even though the games were meant to be played locally only! For that you'll need to have the exact same Dolphin-emu version, exact same ISO file(check file hash to know you do) and same Memory card save if you intend to use that.
Sadly Netplay doesn't work with real Wiimotes(yet...).
From my experience: some just don't work, some work weirdly, I'll try to list what I bought and where and how it works. None store-bought work truly well.
Dongle #1 - Works weirdly but after messing around with it for a bit I got both my wii motes to connect. Would not recommend.
Dongle #2 - Does not work with Dolphin.
Dongle #3 - works perfectly but I don't have an exact link, looks exactly like Dongle #2 but without any text on it or "golden" connector. Seems like it's USB 2.0 V2.0 BT dongle.
The only really functional option is to make your own from a Wii BT chip