If you are facing charges, you probably have waived
your right to not carry a government ID. That's my
guess, but I would talk to a lawyer.
If you are refusing to get the ID on principle,
consider whether it is worth going to jail over, I
suppose. Fill out one of the forms on this site and see
what a lawyer has to say, though. You might be able to
do something about this without putting your name in
the system (although if you are getting fingerprinted,
I'm not sure what you're trying to protect them from
knowing, as you'll be in the system from that point
forward anyway).