I have disabled the profile management on the miniBB. But when I post the message to the forum, there is a link on the username that takes to the user profile:-
forum/index.php?action=userinfo&user=5

Is there a simple way to hide the email address from the visitors? Could not find answer on manuals.

Well, this isn't an answer to your question but something which you might find useful. That link to user's profile page can be removed by editing file templates/main_posts_cell.html. If there's something like this:

{$pLink1}{$posterName}{$pLink2}

Then make it like this:

{$posterName}

Jukkis
If you mean there's an email address shown under the user's profile, it could mean the following:

- The user allowed email to be shown, setting "Show email address to others?" option to "Yes";

or

- While working out your custom membership auth, you didn't put 'user_viewemail' in the table of users, which is a mandatory field for miniBB and which value should be set to '0' by default; i.e. all emails are hidden until allowed by the user. You could also remove this option from the public profile's template, setting it always to '0' in your custom table; but it should be there.