One of my teams wants their customers to be able to reply to the notification email to post a comment reply inside the ticket, but they don't want their customers to be able to create tickets via email. Is this something that's possible? Or is it both or none?
Yes, you can, see https://confluence.atlassian.com/adminjiracloud/creating-issues-and-comments-from-email-779288896.html - note that it lists several types of email "handler". Most of us tend to use "Create or Comment" type handlers, but there are "comment only" ones available too.
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