As of patch 1.04, as you found out, you can turn Weapon Tagging
on/off in the settings, but not the minimap itself, or the radar function.
You can turn off the HUD completely, or turn some elements by applying some unsupported patches to your game. I know, this is not what you asked, but there seems no other way.
This guide explains how you can apply changes manually.
This forum thread lists some of these community patches.
Beware, you might be kicked/banned from Multiplayer games if you play it with these on, so, make a backup of what you are overwriting.
UPDATE: The above mentioned patch files are apparently no longer hosted due-to copyright violations.
UPDATE 2: You can download the patch (for version 1.04) that removes the enemies from the mini-map here.