I assume all previous users can see the correct theme.
Please check the permissions for the file. Somewhere on the way between the site and the file (e.g. at the library level where the file is located) there is broken permission inheritance.
The issue you are describing should affect all NEWLY invited users to the site. It happens because old users had and still have permissions to the file.
You broke the inheritance probably while creating the theme and you wanted to prevent users from editing it. Sorry, but that's the side-effect :( They have to have rights to at least view (pls correct if wrong here) the .js file.
One of the ways to check elements with unique permissions (items, libraries, files) is to go to the Site Settings>Site permissions and view items with unique permissions: