I quite like the idea of the First Order being either the military of the New Republic or a splinter group of it. Them using very Imperial style weapons, ships, and uniforms is sensible considering that the the New Republic would likely have just taken control of all remaining Imperial assets. Plus it ties the New Republic back to the CW era Republic where the white armoured minions and Star Destroyers originated. It’s like poetry, it rhymes.

It would also help sell the idea that the Rebellion/Resistance is the only faction that isn’t a cesspool of corruption and decay (unlike the Republic, Confederacy, Empire, New Republic/First Order, or Hutts). It was always (or at least after the PT came out) daft that the Rebellion wanted to restore the Republic, an organisation that was just as feted as the Confederacy, rather than building something new.

It would have fit nicely with the ‘Let the Past Die’ thing and Luke’s potential moving of Ray away from the Jedi Order into something new, as both the Jedi Order and the Sith are another set of factions that need to be left in the past as their flaws are beyond repair.