What is the use of dual differential amplifiers in audio applications?
Well actually symmetry does play a very big role in why the designer would duplicate (And invert) the selection.

If we take just the top half consisting of the diff pair Q1, Q2 and the cascode load Q5 with the load resistors R11 and R13 you can see that range of operation will be further away from the upper rail due to the Vce drop through Q5.  However, we don't know the currents and values of the various R's so it possible the output pull closer to the lower rail too (but experience tells me not).

So a mirrored system using opposite polarity transistors allows the system to approach both the rails by the same amount.  Closer to one rail would be dominated by on polarity, closer to the other would be dominated by the other.  And indeed in some designs, this approach will allow you to actually drive to the rails.

But symmetry helps in others ways too.

Looking again at the upper stage only, you see that the output will likely also have asymmetrical rise fall slew rate capability.  R11 is what pulls the output high while Q5 is what pulls it low.  I'm willing to bet that Q5 will beat R11 even though no values are given.

The signals "To Second stage" will be complementary and will drive further circuitry (higher output current) to be ensure that the slew rate and thus gain bandwidth, distortion and other parameters are matched.