That is correct for this specific CC. While it is a CC, it's not one you officially own. It's more of a server owned CC. You're free to edit the models and weapons on it, but when it comes to adding things to it, you can't.
If you go to the supporter tab in the F4 menu, you should see a button to switch to the job.
Also no, you can't be a meth cook as a CC. It's basically just a raiding class who can also base.
Lifetime supporter tag can be changed in the same place on the F4 menu