Cannot convert music because protected files cannot be converted to other formats

Have you at any point had a subscription to Apple Music, or could you have purchases from 2009 or earlier? Apple originally sold music with DRM protection in 128k ACC format. This can potentially be burned to CD and ripped back to a DRM free format for a small loss of quality. The rules have changed over time, but at one point if you only had an Apple Music subscription and used this to clone your library to a new computer the new computer would get DRM laden versions of your music. You needed an additional subscription to iTunes Match to avoid this, or to manually migrate your original source library. This is no longer the case but if you moved you library when it was then you could be affected. Take a look at the media kind of the affected files. Do they show as Protected AAC or Apple Music? What is the iCloud status of these tracks? Purchased (post 2009), Matched or Uploaded tracks should be available to download in 256K DRM-free AAC format.

More recently Apple have introduced lossless streaming and downloads. These files are always protected. You may be able to turn off the option to download lossless files, select and right-click a selection of tracks and click Remove Download, then right-click the same selection and Download to get DRM-free versions of the same provided these show as Matched/Uploaded tracks rather than as Apple Music.

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GwenH Said:

"It appears that all of the music (including itunes downloads and cds) were all brought over as m4p protected files. A playlist that I created over 10 years long before I subscribed to Apple Music subscription are all now m4p protected files. When I attempt to convert them to MP3 files (from the Music menu [File-->Convert-->Create mp3 version]) results in an error message '...could not be converted because protected files cannot be converted to other formats'."

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Changing a Personal File's Extension:

What's the source of these when you created this library long ago? That may be the issue here --it seems this is being seen as if it is piracy. So, try using that app is the way to go about this. Try using another device --perhaps a PC? Also, create a different Administrator User, seeing if your can do so there.