Doug, while law enforcement hopefully will not mess with any of us. The fact that that your car can be towed for a fix-it ticket is real. An example is that if your
oil pan is lower than the bottom of your rim height which is a simple fix-it ticket. Added to that cite is 24002cvc, unsafe vehicle, which orders the driver to immediately take the car to a repair station or park it within a reasonable time from the date and time of the issuing of the cite. The next time the car is seen moving without the violation being corrected, the car can and probably will be hooked.
As far as registration goes, a cite for expired reg is also a fix-it cite of sorts. But, wait six months and the vehicle code states "must take", which leaves discretion out of the quotient.
For things like excessive noise, you can be cited (and in Monterey will be) for simply cruising in a low gear making about 100 db or less ( I can’t remember the max Db level....93, 97, somewhere around that). It has nothing to do with the fact you're driving a replica or smog exempt vehicle. Many out there think because it's a copy of a '65 it falls under the rules of a '65.
Were able to run some of the equipment we do because law enforcement generally WANTS to look the other way because most of us are not hooligans...well maybe I am, a little! There are numerous violations on these cars as soon as they hit the street. Just drive up to an officer and say "you can't touch my car because it's had all the inspections and besides, it's a "65", and see what happens. I don't think in '65 you were required to run a front plate in Ca. but you are now and so is replica of a '65.
I hope this answers your question. I may have overstated things a little. I just feel lucky to be here and still able to own one of these cars knowing what I know.