I managed to sidestep this issue by deleting myself from the list of testers and creating an external testing link. Using that link resulted in TestFlight correctly displaying the game instead of being stuck in the "Redeem" dialog.

I solved this by aborting the review of the version I had submitted. This allows the build to be changed in the app, then start a new review.

Solution that worked for me: Log into appstoreconnect.apple.com Access your app. Go to TestFlight tab Locate the group on the left where that user is part of Remove the user by pressing the checkbox, followed by the "Remove" button Add the user back by pressing the blue (+) button next to "Testers" header. Choose "Existing" and choose the user from the list. Their TestFlight should refresh with access to the app.