There's an update to the OverDrive app that eliminates the Adobe ID so instead of seeing the prompt to create an OverDrive account and then having to create an Adobe ID (requiring the customer to leave the app, go to Adobe's website to create the ID, then come back to the app), customers reinstalling the app or installing it for the first time will only see the prompt to create an OverDrive account. And if they don't want to create yet another account to remember, they can authenticate with their Facebook account:

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Nothing will change for customers who currently have the OverDrive app authenticated with an Adobe ID. I updated the app on my phone to verify that this is the case. And if a customer wants to get rid of their Adobe ID (and I would suggest they do this without having any titles checked out because titles originally checked out to their Adobe ID are not available to be read with their OverDrive account), they can deauthorize the app and reinstall it using only the OverDrive account.