My Mac unexpectedly updated itself to Safari 11 the other day when I wasn't paying quite enough attention, and the SugarCube story I'd been working on without issues until now stopped opening in Safari, with the error SecurityError (DOM exception 18). I tried both SugarCube 1 and 2, and both gave the same error; it just looks nicer in SugarCube 2.
I googled and only found an old error with SugarCube that was similar but not the same thing. I did find an answer eventually by looking for non-Twine-related advice about the error; since I'm opening the generated files manually I now need to select "Disable local file restrictions" from the Safari Develop menu to get the story to work. It's not an issue when the story is hosted on a web server.
If you don't have the Develop menu on, you need to turn it on in order to access the relevant setting.