If you go to the https://www.+++academy.com, scroll down and click on "My+++land" link in the footer, you'll be taken to "Protected Content" page with a login form. When you try to login there using test user (see additional notes in chat) you'll notice that port number :80 is added to URL resulting in a redirect to non working site.
It's been suggested that it's something wrong with SSL certificate implementation but WP Engine confirmed that it's setup fine. They were also able to replicate the same issue on a staging site and run a full conflict test there but it didn't help in any way.
The .htaccess is default apart from "Prevent Information Disclosure" rules added by Defender.