Should I be concerned with the group phase delay which a filter produces? Especially in an audio application? Should I aim at using a linear phase delay filter for example?
i will agree with Hilmar that it can depend on the specific application.
if the application is to essentially losslessly store or transmit audio to later retrieve or receive that audio, including conversions of format (and this includes the A/D and D/A and SRC) then i would say that there is no good reason for a process to not be linear phase (which is constant group delay, constant phase delay, and the two constants are the same number). there are audio format conversion processes (like a lossy codec) that are meant for storage or streaming that, for the sake of data reduction, have non-constant phase delay or non-constant group delay.
so if the application is to change the audio in some manner, it might not be possible to have the entire transfer function to be linear phase because of feedback.
if there is never any feedback and the audio is passed from one process to another, in cascade similar to the figure above, and all processes are meant to not change the perceived sound, then each process can have constant delay and there will be no waveform distortion due to non-constant phase delay or non-constant group delay (non-constant delay would not be a linear phase filter). so in this non-feedback case, there is no necessity to ever make different frequency components have different delays, and i would suggest to normally make that application linear phase.
sometimes, there are audio application in which a the process is one of several in a feedback loop, such as a feedback exterminator or maybe some reverberation control, it might be in this application that you might be tuning for a specific non-constant phase or group delay.
there are also applications like musical effects where a non-linear phase shift might not be perceptually relevant, but we know that linear phase shift is perceptually irrelevant when the processed sound is not compared directly with the input sound, so that the delay is detected.