To me Grim Traveller poses a very grand question: "Are there any songs that contain subjects that you are so opposed to that you won't listen to that song?" that for me seems to address the importance of a song's lyrics over the musical composition of the song, so for me this question is about the written word independent of the musical composition.
I am always amazed at how good songwriters can merge two major means of artistic expression into a homogeneous whole. Of course pure instrumentals stand alone, and lyrics, which are poetry if they are written in that manner, or of prose and storytelling if written in that manner too, and those stand alone too. This is in effect of course a highly subjective subject about the written word, yet in a way it is essentially like asking about what the mere nature of music too -- the epistemological question about how do we understand the essence of music?
The lyrics have to be offensive to me or neglectful of something of great importance to me. A local songwriter parted ways with me after he wanted me to listen to his new song about the courtroom expression on the face of the sentenced for life police officer who knelt on helpless George Floyd's neck and thus strangled him while he begged for his life. In his song there was no regard for George nor the expression on the faces of George's loved ones etc. I couldn't like the song because of the lyrics. Sadly we live in very divisive times and no way could I enjoy his song.
Then there are lyrics to songs I like that are very simplistic about love, that in a way could be almost embarrassing for an artist to sing. I think of like songs from Diana Ross and The Supremes, like "Baby Love" etc. but when I heard The Supremes I was simply very impressed. "They swept me off my feet ha! I remember an interview about The Supremes and how they didn't want to sing about such simplistic themes but the manager at Motown dictated that was what they must sing, no questions asked. I doubt just about everything as I judge my own original music and now a year later on YouTube and my songs stagnate, so who am I to say anything ha! I hope I helped in some small way.