Single handle shower faucet from the 80s making loud noises
High velocity flow through a restricted opening connected to a resonance chamber causes whistling.  Things you might try other than modifying the valve:


Install a flow restrictor at the shower head.  It only needs to restrict the water a little to change the dynamics of the flow through the valve.  If you start with one that restricts the flow so much it is annoying, you can usually enlarge the opening in it with a drill.  Of course, if you enlarge the restriction too much then you will be back where you started.
Check system water pressure.  If it is above 60psi, then consider installing a pressure reducing valve on the system.