Listen to shape note singing. Folks pitch each song to taste. If it doesn't cure you of perfect pitch, nothing will.
funny thing your post reminded me of. Was doing a touring production a long time ago when an accompanist who is still a good friend transposed one of my arias on the synth and everyone offstage could see me squirming and working REALLY hard not to lose it. Things felt weird and notes that were easy became hard and passages that were hard were made easy. Felt soo weird.
I did barbershop and a capella stuff for a longtime and I can deal with it but it sometimes felt like nails on chalkboards.
Next time your at a public performance of something that has some bad notes look trough the audience. Everyone with a good ear either squirms or their posture gets really good and they raise their heads up like they are trying to will the note where its supposed to be.