Our organization is hosted - I have not seen a way to do this! The only way we've managed to share information is to create an ArcGIS Online group > and then if the outside user has an ArcGIS Online account, you can add them to the group and then can access the data that way. Permissions on ArcGIS Online need to be able to allow for outside account access.
Side note - I don't actually allow this anymore because I discovered that if you allow an outside account access to something on the hosted Online site, there is really no way to limit their permissions or kick them out. As admin, usually you can add/remove people or transfer ownership of things - but if an outside user creates something and shares it to our side, then I (as admin) lose access to control it because it's created by a non-hosted account. That outside account also has the ability to see everything that is "organization only" on the site. If the outside user creates something on our site, there is also no way to transfer ownership from the outside user to someone at your org.
So in a nutshell - I would not recommend it if the hosted site has any time of sensitive information! Because there appears to be no way to limit permissions to the outside user once they gain access to something. Even on the admin role 😬
