Customize Apple Music to censor bad words when displaying lyrics

It is the Rights Owner/Publisher of the music that chooses the Explicit/Clean version of the song they want available on Apple Music. A clean song submitted to Apple Music will include the clean lyrics. If you want a song available in Apple Music as a clean version, you would need to contact the Rights Owner/Publisher of that song to have it available. It is their choice what songs they want available and Apple is not censoring any of the copyrighted material to make it clean. Most songs that are Explicit also have a Clean version, but again, it is their choice, not Apple's to sell those songs or make them available for streaming.

You can certainly send feedback to Apple here for any such feature:

Feedback - Apple Music - Apple

To be clear, the lyrics you see are what was included with the Metadata provided by the Publisher of that track. Apple is not changing any of the lyrics that are sent to them, so any censorship on a particular word is done by the Publisher. It seems if you choose to listen to Explicit content, there would not be a problem with reading explicit content. The answer to that is clearly to choose the Clean track when available, but I do understand you still want to listen to the Explicit content.

If Apple can provide a way to show the Clean lyrics on an Explicit song where both version are made available, the feedback link may be the way to go. Although with some songs, there is quite a difference between the Clean lyrics and the Explicit lyrics with entire sentences of the songs being different and in some cases complete sections are cut out.