My understanding of FCC rules on CB prohibit the use of such for political and commercial purposes.
In case you still respect the law that is.
I suggest everyone contact their Secretary of State or appropriate authority and take every legal measure at terminating your DL, then reapply using every religious objection possible, but do not assent to ID using your name, SS, or picture, instead offer as a proving mechanism the print of your big toe under conditions of use limited to validation of the holder of the license.
There is no reason the state cannot both protect your identity and certify you as a safe driver.
If you have no proof of ID, how can you obtain one? If it doesnt exist, it doesnt exist.
I don't know about the rules expressly prohibiting politcal activities - but CB was established to facilitate 'bidness' ...
Now, the rules on amatuer radio *do* expressly forbid 'bidness' use of same.