Publicly (in other words, to the best of your inRP knowledge), the Crayter Republic maintains a neutral stance to the Imperial Kusari Exiles.
However, CR does not like the Imperials because it is the Emperor who first declared war on us. Sure, the Republicans continued it and we now face Gallia, but there's no guarantee you won't continue your aggression against us once/if you take back control over Kusari. Also, CR never signed the treaty that you made with Bretonia at Leeds, back in 820 AS.
Essentially, the Crayter government and military leadership is of the opinion that Kogen messed up, and crawling back to us now is no way to gather friendship, nor support. We're actually looking to support the Shogunate side of the Kusari three way civil war.
Not that you'd know (could maybe speculate) that inRP, of course, but this is our standpoint. Again, publicly, we're neutral, though you may eventually feel the "cold shoulder" of our actual unfriendliness as the Kusari mess unfolds.
Posting on behalf of CR| as SiC; Minister of State