I think I understand what you're saying, and I can relate to a degree. Cringe lyrics or other people's opinions don’t usually influence my enjoyment of a song either.
However, there are exceptions. For example, XODIAC's "Lemonade" is one of those songs I struggle to enjoy because it’s so repetitive—it’s literally just the word “lemonade” over and over. In cases like that, it does affect how often I want to listen to it compared to their other songs.
As for "cringe" lyrics, I tend to chalk that up to non-native English speakers trying to appeal to international markets. I don’t necessarily blame the artists for that since they’re doing their best to connect with a global audience.