I found an effective workaround for ensuring Apple Music playlists are shuffled as part of Alexa Routines.
It involves buying a cheap Airport Express from EBay (about £50) Apple no longer sell the Airport Express but still supports the firmware. You will also need a smart plug that supports both Siri and Alexa like Meross for example. I have a automation set up in the Home App on my iPhone that when my speakers are powered on by a Meross smart plug (in my case a Bose speaker but any speaker connected to the Airport Express by a aux lead) a Apple Music playlist will play shuffled properly.
I like the solution because it bypasses the broken Apple Music Alexa skill but remains part of the my Alexa eco system and routines. For example, I can say “Alexa, Good Morning”. Alexa switches on the Meross plug which in turn powers on the Bode speaker and triggers my Apple Home app automation to play my playlist SHUFFLED!
Total cost of the workaround £65.00. As an Apple Music subscriber who likes to play music shuffled properly every morning this is money well spent. I also enjoyed the challenge of finding this solution.
Aside from playing playlists shuffled as part of an Alexa routine I did opt to add a HomePod Mini to my predominantly Alexa home. Heresy, I know, for Alexa users! However, for Alexa routines and Apple Music playlist shuffling the HomePod Mini is not essential, as far as I am aware.
I know this hassle and extra expense won’t be for everyone. I just wish the workaround wasn’t necessary and in the words of Steve Jobs Apple Music on Alexa just worked!
Come on Apple, fix your broken Amazon Alexa Apple Music skill!