"did most people believe that they were supporting a just cause or were they lied to?" - Gnome - you are asking the wrong person the question - With apologies to Mr Suffet and to quote from his excellent song:

"Ask the people of Belgium, or Alsace-Lorraine,
If my life was wasted, if I died in vain.
I think they will answer when all's said and done
That they welcomed this young man with a tin hat and gun."