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Hi Ivan-Brhuehue,
Thanks for the detailed description from your end and I apologize for not being so clear from our end about the external sharing user to sync the shared document libraries in the SharePoint Online.
Personal account users like Gmail.com, Outlook.com, Hotmail.com etc. can’t sync the Document Library of the SharePoint Online provided the Business organization where they can only view or access them in the browser. The possible reason is SharePoint Online Document library is linked with the OneDrive for Business, since the personal users doesn’t have the OneDrive for Business, they can’t be able to sync it.
External users with the Business account like contoso.onmicrosoft.com are be able to sync the Document Library shared by the other organization without any problem.
To your scenario, as the external users are having the Gmail account, we are sorry to convey that they are not possible to sync the Shared document libraries on their apart from accessing in the browser.
I do understand the inconvenience caused at by the external users end and apologies for it.
As a workaround, if you want the external users with the personal account want the folders in the SharePoint Document Library to display in the File Explorer of their Windows device, you can allow them to make the SharePoint Document Library as a Network Drive. Here is the reference article: Mapping a SharePoint site as a network drive.
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Hope the workaround helps the external users and thanks for your understanding!
Best regards,
Gloria