This is one of those terrible user experience design issues that you see all over the place these days. Yes, Microsoft stuff is full of them, especially the cloud services, but then so is pretty much everything else. Sarcasm is turned up to 11 on this post.
Your users need to be able to share links to items in OneDrive for Business just via an anonymous link. Yes this is terrible from a security point of view, but business needs must and all that.
So you check in SharePoint Admin Center – Policies – Sharing:
Well the sliders are both all the way to the top, Content can be shared with anyone, so you think to yourself “WTF?”.
It all looks good, and you notice that you need to be in a group to share externally, but you (or the user with the issue) are in the group and have been for ages.
Well, due to some unnecessarily bad design, you also need to click the Manage security groups button. Because in there you can set the degree to which members of that group can share externally. Those pretty sliders that say Anyone? Zero effect now. Displaying the group name and the permissions in a table right from the External Sharing policy page? Nope.
So change that Can share with setting to Anyone, remember to click Save down the bottom, and after some undefined period of time (Seconds, minutes, hours. Days even?), you might find that users can now finally select the Anyone with the link sharing option. It might be worth getting them to hit F5 to refresh the OneDrive browser page – but this might not be necessary.
But before you leave the SharePoint Online Sharing Policies page, scroll a little further down and check out the section titled Choose expiration and permissions options for Anyone links – you might want to change those settings too: