Hi,@Shawn Imholte
Thanks for posting your question in the Microsoft Q&A forum.
Based on your description, you are using Azure to host Exchange Online. i am not sure if it is Azure that is affecting the use of Add-DistributionGroupMember. Can you describe specifically how you are using Add-DistributionGroupMember? It is recommended that you disconnect Azure Hosted Exchange Online first and only run commands in Exchange Online PowerShell.