Here is how to open a Google Shared drive to share with people without @uw.edu credentials
Right click the shared drive and go to "Shared drive settings"
In the next dialog box, check the top two boxes.
(Be careful, the second check box will allow you to add anyone, even people who aren't members of the top level of the drive. This setting makes it easy to add someone, and likely forget to ever remove them!)
Once you've checked these boxes, any folders inside the shared drive can have people with @gmail.com addresses added.