Two mandatory conditions? It does not work ..

[ZiNgA BuRgA]

You need to think through your logic.

For THIS_SCRIPT != "member.php" AND $GLOBALS['mybb']->input['action'] != "register"
- member.php?action=register: THIS_SCRIPT is 'member.php' so condition is false
- member.php?action=login: THIS_SCRIPT is 'member.php' so condition is still false

For THIS_SCRIPT != "member.php" OR $GLOBALS['mybb']->input['action'] != "register"
- member.php?action=register: THIS_SCRIPT is 'member.php' so first condition is false; action is 'register' so second condition is false, meaning whole condition is false
- member.php?action=login: THIS_SCRIPT is 'member.php' so first condition is still false, but action is NOT 'register', so second condition is true, making the entire condition true

Note that
!(THIS_SCRIPT == 'member.php' AND $mybb->input['action'] == 'register')
is identical to
THIS_SCRIPT != "member.php" OR $GLOBALS['mybb']->input['action'] != "register"
(De Morgan's law)