I have a web app that I would like to share with individuals from outside of my organization. The other organization only has a public account (no subscription to ArcGIS online). Is it possible to add their usernames to a group that I have created so that I can share specific content with them? If this is not possible, what options do I have to share the web app with their organization? I read something about a "viewer" type user, but I do not know if I have the ability to set one up. The information is sensitive, so I cannot share it publicly.
Adding Public Account user to Private groups is not allowed by design. Following options can be explored;
1. Share the Web App and subsequent layers publicly and allow anonymous access in organization., Check this documentation.
2. Add users who needs to access your organization as Viewer (formerly Level 1) users. This blog might help you to be familiarize with Viewer type.