Last tested: Nov 18, 2020
Firstly, if we open up the network tab do we see a 3xx redirect when trying to load the topojson file? And does that redirect back to /login?
If so next we will want to check if while logged in to Looker in the same browser session does the public look load without issue? Though public looks are meant to be as it states, public, if we are using a custom map layer that is defined in Looker (ie. only accessible from within Looker) then the only way to fetch it is by having an authenticated browser session already open.
Next steps, host the json file literally anywhere else (github, etc.) somewhere that is publicly accessible. Point the map layer to the url path of that file and boom, should load without issue!