I am sorry but could you give a link to the source where it is stated that mages can close tears. And how does staying neutral results in Fereldan being invaded?
Mages can close the Veil tears, or spirits or even demons, if they cared enough to do so.
Codex:
It is theorized that the Veil tends to be weaker in places that feature (or have experienced) extensive death and or use of magic. What is known for sure is the use of blood magic can allow the Veil to be opened completely so that demons may physically pass through it into the physical world. Areas that can be seen or felt where the Veil is thin are usually referred to as 'Tears' in the Veil (in keeping with the fabric metaphor). 'Mending' these Tears (i.e. strengthening the Veil) is extremely difficult , especially for those unfamiliar with the area.
For example, in Soldier's Peak, either Sophia Dryden or Avernus can accomplish such a mending (Avernus being the likely source of the tear with blood magic, can mend it with blood magic, and Sophia being a powerful abomination who has remained in the vicinity for centuries).
There is no hope to close a Veil tear without either a mage, demon or spirit. Since the latter two are very rare to help Mages are your best bet.