The scene when the First Order fires their weapon the first time in Star Wars: The Force Awakens uses an image language which clearly references the national socialism in Germany during World War 2, with a general making gestures and shouting like Hitler. This even depicts the stormtroopers raising their arm and shouting in a way untypical from the original trilogy.
Has the reason why the director of the film chose this style ever been explained?
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.
His line
"...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.
I think the point is "we're supposed to be uncomfortable". The very fact that the origins of the word stormtrooper come from German (Sturmabteilung) but came into common use in WWII as some of the most brutal of the Nazi regime soldiers ought to be a clue, plus the cut of the uniforms all the way from the beginning were very similar to the SS cut.
The Nazi's were genocidal -- the Empire/New Order think nothing of blowing up planets as an intimidation tactic. The look in the general's eyes when the planets go up in the Force Awakens is somewhat terrifying, yes?
Thirty years later (another generation has passed) and your references to hokey, ancient religions or political schemes must be more anvilicious to be recognizable to princesses, scoundrels, and farmboys.
(I was born a little too late to directly experience the fear that "the Russkies" were going to "nuke us all". I certainly received a large dose of it as received wisdom and everyone I knew was certain "the Reds" would start a nuclear war. But, it was a little abstract even by the mid-'70s, when my reliable memory starts. The college students I teach now have literally no idea what it is like to be that afraid of nuclear war. It's a total abstraction for them. If you want to raise this referent in their minds, you have to do so much more extravagantly ... and they're still not convinced that the threat was credible.)
We must also remember that a lot of star wars was inspired by the ancient religion hinduism - george lucas himself seemed to have been inspired by many ancient hindu texts. Starting from names such as Yoda (Yoga) Darth Vader (sound like Veda - which is the ancient hindu text) and the Swastika symbol which hitlor adopted but has long existed as the symbol of hinduism.
