Alex, the main problem in what I describe above is that you can see the profiles completely, even though in #permission, "View profile" is off for unauthenticated level.
There is no message in this case, the profile is visible by being non-member.
And I add that in this case, out of 12 profiles, two are not visitable(not clickable) and all the others yes. Why?
Visit this page to see the problem please.
https://una.twoforlife.com/page/persons-home
Go to the second page, baloo and goldenboy are blocked (not clickable), all other profiles are visitable.

All profiles should be clickable and a message should appear, no matter which one.

Currently, you are obliged to go through "Pages" and disable all the blocks one to one for the non-connected, that is not normal.