I just had this issue, where I had a multiple dashboards embedded in experience builder, where some dashboards required a log in, and some were just fine. I found that it depends on which link you use for the embed. It seems that when I use the URL that the metadata provides shown below, it causes the issue for users to log in.
MapExplorer_27_1-1730229517199.png
Whereas if you use the URL directly from the dashboard page, the login issue disappears. Hope this helps!