Under a SharePoint Online document library, is it possible to share a folder with external users without sign-in?
The "no sign-in required" option is available on files, but not folders.
No, it's not possible to share folders with "No sign-in required" at this moment. Anonymous links are available only for individual files or document. In future updates to Office 365 it will be available. Do keep checking the messages in your Office 365 admin center.
Also, usually this update will be rolled out initially to "First release" users. So you can setup your tenant to receive the latest Office 365 updates.
Reference - External sharing with Office 365
Uservoice - External Folder Sharing with without sign-in
This feature is yet not available in SharePoint, but product team has confirmed that they are working on this feature...below is comment from SharePoint User Voice forum
WORKING ON IT · SharePoint Experiences Team ADMIN SharePoint Experiences Team (Admin, Microsoft SharePoint) responded · May 10, 2016 Thanks for your feedback! Just a note to let you know that we like your suggestion—to allow external folder sharing without requiring recipients to sign-in—and are working on it.
Within this thread, we also heard feedback that we should simply our account creation process. We listened to your advice, and have a new and improved lightweight sign-up experience, which you can see here when you click “Create Account”: https://account.microsoft.com/about
below is link to refer full thread around this.
May be you can also raise your voice so that they can make it available soon. :)