What is the purpose of the little yellow plastic disc that comes installed behind the cylinder on a new Super Redhawk?
I don't know, exactly, but the manual states specifically that the disk should NOT be left in place while dryfiring.
Can Super Redhawks be dry fired without damaging the gun?
Yes and no.
Dryfiring operates the action and causes wear, just like operating the action while shooting the gun. Enough of it will cause parts to wear out and break, just like operating the action with live cartridges will. Admittedly, wear due to recoil is eliminated during dryfire, but there is other wear & tear that takes place during dryfire and normal live fire. I would just say no, but I worry that someone would see that and dryfire their gun hundreds of times a day every day and then complain after years of maintaining that kind of practice schedule that the transfer bar broke and Ruger is lying when they day it's safe to dryfire the gun.
However, dryfiring a Ruger SRH will not cause anything other than normal wear and tear to the internals. It's not like some guns which can be broken or permanently damaged by dryfiring just a few times.
From the online version of the Ruger Super Redhawk Manual.
https://ruger-docs.s3.amazonaws.com/_manuals/superRedhawk.pdf
DRY-FIRING
“Dry Firing” is practicing the trigger pull of the empty revolver for practice and familiarity. The Super Redhawk® revolver can be dry-fired without damage to the firing pin or internal components.
Be sure that the revolver is unloaded before handling. Be sure of your bulletstop, even when dry-firing for practice. Do not dry-fire the revolver with the plastic ‘safety disc’ on the cylinder.