No, the diodes are *NOT* there for incoming reverse polarity protection. They are there to protect the regulators and load if one of the unregulated input supply rails goes missing, e.g. due to a blown fuse.
Consider what happens if the -20V input is lost while you've got a load of a board full of OPAMPS drawing say 300mA. Due to the current through the load, the regulated -15V rail will rapidly rise above ground. You've now reverse biassed the 7915 regulator's internal circuits between Out and Gnd, and probably damaged it. Also all the OPAMPs in the load have had any grounded inputs taken well negative with respect to their Vee pin, so the odds are high that they've been damaged as well.
Re-connect the -20V supply and the 7915 may well let it straight through unregulated due to the damage, and half your OPAMPs are already 'pining for the fjords' and cant wait to 'elect a pope' as soon as they get power to do so. %DEITY% forbid you've used Tantalum decoupling caps - if so, after a reverse polarity insult, you'd better have a fire extinguisher handy at the next powerup.
The diodes prevent all the drama by limiting rail reversal if one input supply is lost to about 0.6V-0.7V at which voltage, parasitic PN junctions in ICs wont be forward biassed hard enough to pass enough current to damage them especially if the pins in question have any series resistance. If you want to be *REALLY* certain, because you've got a particularly electrically delicate and high value load, use Schottky protection diodes across the regulator outputs to limit rail reversal to under half a volt.
Even more fussy circuits may need power sequencing, but that's highly unlikely to be needed in an audio application that doesn't do DSP signal processing.