You have to install MP3tag with a portable installation that saves all settings in the installation folder (here: on the sd card).
If you install it the "standard" way, then all settings stay in the appdata folder on the local computer.
Edit: if you have a look at the data folder of MP3tag, you may find a file
genres.ini
This file contains user-defined genres as set in File>Options>Genres
Copy this file to a temporary location, install MP3tag as portable application, then copy the
genres.ini
into the data folder of the portable installation.
Like this you should get your user-defined genres.