Everything is working exactly how it should.
Mario Kart supports BOTH "GameCube Controllers" and "Wii Remotes".
By having BOTH configured you are emulating a "GameCube Controller" and a "Wii Remote" at the same time using the same physical gamepad, which is probably not what you want.
E.g. When you press "Button 2" on your Saitek gamepad the game sees BOTH a "GameCube Controller" pressing "A" and a "Wii Remote" pressing "A" because that is what you told Dolphin to do.
Mario Kart supports BOTH "GameCube Controllers" and "Wii Remotes".
By having BOTH configured you are emulating a "GameCube Controller" and a "Wii Remote" at the same time using the same physical gamepad, which is probably not what you want.
E.g. When you press "Button 2" on your Saitek gamepad the game sees BOTH a "GameCube Controller" pressing "A" and a "Wii Remote" pressing "A" because that is what you told Dolphin to do.