I am a "music first audiophile". I would be hard pressed to not listen to a recording where I thought the music was great, but the recording, not so much.
Lucky for me, the 3 genres (classical, prog, jazz) and their various subgenres I listen to, tend to be recorded better than average.
So, I have very few bad recordings. But, for me, the music is more important, so I will listen to bad recordings, for the musical content.
I do tend to give a bit more priority to good sounding recordings, however. But not for the reasons most stereotypes of audiophiles would describe*, but because I find it easier to become more emotionally and/or intellectually involved with the music.
Let me add, that I do tend to disagree a bit with @rvpiano concerning the sound quality of classical recordings. I tend to find the majority of them to be quite good. I find it easier to find good sounding classical recordings, that band ones. Especially with regards to soundstage and imaging, the natural ambience of the acoustic space where the musicians were playing, and other spatial cues.
But then, the vast majority of the classical music I listen to, is from the 1950's up though the current era. So, I have the advantage of a very high percentage of it being recorded on good gear, with modern miking techniques.
*the quote attributed to Alan Parsons is what I am referring to: “Audiophiles don’t use their equipment to listen to your music. Audiophiles use your music to listen to their equipment.”