When logged in as Admin and writing a new entry, I get a drop down menu with categories and text field for tags.
When logged in as User, the text field for tags is missing.

O.K., I had a look at the code. Simple users cannot use tags, and that is no bug. Its intended by design.

to change this behaviour, I needed two modifications:

In forum/themes/default/subtemplates/posting.inc.tpl, line 119

change {if ($admin ||$mod) && $settings.tags} to {if ($admin ||$mod || $user) && $settings.tags}

That opens a textarea for tags for registered users != mod or admin.

Further, I changed in forum/includes/posting.inc.phpm line 643

if(isset($_POST['tags']) && isset($_SESSION[$settings['session_prefix'].'user_type']) && ($_SESSION[$settings['session_prefix'].'user_type']>0))

to

if(isset($_POST['tags']) && isset($_SESSION[$settings['session_prefix'].'user_type']) && ($_SESSION[$settings['session_prefix'].'user_type']>=0))

(The only difference is an additional '=' near the end of the line)

That feeds the tags to parser/database.

I hope I did not damage any other function by my modifications