2.1.5 [WEBSTG] Section 4.5, Threads
The specification states:
Because of the use of the storage mutex, multiple browsing contexts will be able to access the local storage areas simultaneously in such a manner that scripts cannot detect any concurrent script execution.
IE8 Mode, IE9 Mode, IE10 Mode, IE11 Mode, and EdgeHTML Mode (All Versions)
The storage mutex is not supported.