There's no GMG conflict.
There's no GRN in Taus.
There's no CR fighting KNF (And even right now, KNF didn't declare war in CR; it's was just their declaration, and even then, they can declare whatever they want, but that doesn't mean KNF has wasted any resources for a war of words).
Now, if the lore has changed, I'd like to know why does it only changes for KNF.
Let's say we move a bit further for 4.86 lore, then it shouldn't involve only GRN. It should move for every faction. That would include corsairs in bretonia.
And since there's no 4.86 lore regarding KNF and GMG, and considering it's not a war, but a small conflict (which can be checked by the actions in game, from zero to none), I'd not say KNF is using a lot of resources with GMG.
And you don't really want to use the Player Role Play here. Because I've seen far more GRNs shooting BAF than KNF.