It isn't just in The Force Awakens that this is the case. The original trilogy drips with it:
George Lucas has also stated that he sees the rise of the Empire as an allegory to the rise of Nazi Germany and that the uniforms are based on German officer uniforms.
The Force Awakens is just carrying on the theme previously set in the original trilogy that the Empire is a Fascist regime and as such borrows from the most famous fascists of them all, the Nazis.
The Force Awakens may lean more heavily on this as they are the remnants of the empire made up of the ultras, the true believers, and as such want to push the ideology to the forefront of what they do.
Also as with Nazi Germany, the Empire probably did not see the need for mass rallies having cemented their power (the Nazis stopped the Nuremburg rallies in 1938), but with the Empire crumbling, the Emperor dead and their ideology threatened the First Order can use it to keep everyone believing.
In a Time article JJ Abrams specifically mentions the parallels to Nazism in The Force Awakens which follows the same ideas as my speculation above.
"...what would have happened if the Nazis all went to Argentina but then started working together again?"
Shows us the First Order is how he thinks the remnants of Nazi Germany would have gone had they tried to rebuild out of the ashes.
(Looking at the two pictures below only the scale has changed and flags have been added, probably to make up for the red missing due to the absence of the Imperial guard).
Return of the Jedi - Palpatine arrives
The Force Awakens - speech on Starkiller base
Both images bring Nazi "spectacles" such as the Nuremberg Rallies to mind.