Using New Outlook on Windows for personal email, calendar, and contact management
Hello K McMaster,
Thank you for posting this case in the Microsoft Community!
Based on your description: Your auto-reply is not working for outside your organization emails. If someone emails from within the organization they get an auto response. If you get an email outside of the organization (ie a Gmail account) there is no auto-response. I would like to cooperate with you to work on this case. To clarify this case, are you using New Outlook for Windows or Classic Outlook for Windows? For my suggestion, if using New Outlook for Windows, you may check if Send replies outside your organizationoptions are enabled and auto-reply email template is set up or not. You may go to New Outlook>Settings>Accounts>Automatic replies to check further. You may check this Microsoft article as a reference Send automatic out-of-office replies from Outlook for Windows.
If you are using Classic Outlook, you may check if Outside My Organization(On) - Auto-reply to people outside my organization & Anyone outside my organization enabled and set up normally as below captured. You may check this article as reference Set-up auto-reply (out of office).
As suggested, you may try to set up auto-reply in Outlook Web if working or not Send automatic out-of-office replies from Outlook.com or Outlook on the web. If this case only happened on New Outlook for Windows with the correct settings, please contact the New Outlook for Windows Support Team by clicking Help>Contact Supportor Contact support and provide feedback within the new Outlook for Windows. The support team over there has higher permission than us, they can remotely help you and collect logs at your convenience. They can also involve more resources to investigate the issue from the backend side. This would be the most efficient way to handle this case for you.
Hope the above workaround will be helpful. If you need further assistance, please feel free to let me know, and I will keep assisting you.
Your understanding and patience will be appreciated.
Regards,
Microsoft Community Moderator