Last tested; Sep 15, 2020
Looker Login UI will always require some sort of login state, even public Looks. Looker UI needs to create a session with a "fake" login for the anonymous user viewing the public content and Looker UI needs to save this login state in a browser cookie.
If the content is coming from a 3rd party domain, it will require a 3rd party cookie.
The best way to avoid this problem will be to change the domain name.