If you are seeing a message when using a Power-Up that you aren't able to authenticate because your browser's localStorage is disabled, this article shows how to fix that in Chrome.
On this page you will want to check that the top toggle, to "Allow sites to save and read cookie data" is enabled. If it is disabled, and you want to keep it that way, you can also add exceptions here, by clicking the "ADD" button to the right of "Allow":
Enter the domain to allow, in the screenshot above, we allow localStorage for all Power-Ups made by Trello.
To make these changes in Firefox, you can go to "Preferences" > "Privacy" > and then "Exceptions." There, you can add an exception for the service you want to allow, though you won't be able to use wildcards as in Chrome, so you need to be explicit in the correct address, such as "https://github.trello.services."
Additionally, Firefox will default to http, so you also need to specify https for the exception to work.