If you see a blank screen or you are having issues with Phantom extension on Firefox browser while using Private Browsing, this is due to a limitation of that incognito mode. To be able to use Phantom you'll need to manually set to true the dom.indexedDB.privateBrowsing.enabled setting that you'll find by navigating to about:config in the address bar.
If you need help, go to https://help.phantom.app/ and use the live chat button at the bottom-right corner.