If anyone else is wondering, I’ve not found a verbatim quote of the steps but I did see an article that mentioned the consequences. It seems like you will be able to turn this off but it will disable Voice ID:

anyone with their Echo device set to “Don’t save recordings” will see their already-purchased devices’ Voice ID feature bricked. Voice ID enables Alexa to do things like share user-specified calendar events, reminders, music, and more. Previously, Amazon has said that “if you choose not to save any voice recordings, Voice ID may not work.” As of March 28, broken Voice ID is a guarantee for people who don’t let Amazon store their voice recordings.

If you do not want to set your voice recordings setting to ‘Don’t save recordings,’ please follow these steps before March 28th:

Am I the only one curious to know what these steps are? The image cuts off the rest of the email.