As the title asks, does the Religious choice offer alternative paths to choosing Military playing the Hissho? This patch seems to be about warfare, but there is the hint that Religious vs Military offers different possibilities

 Their questline certainly have quite a few religious choices, and at least right now with the economic behemoth apparently bugged, economic and science victory are easy enough. 

 That being said, due to the nature of Keii, avoiding combat altogether is impossible or at least massively inefficient. They have a very low limit of colonies without the keii costs becoming absurdly high and unless there's a religious law I'm not aware of, combat is their main method of expansion. 

 Basically they are terrible neighbors. 

Annoying birds...always sqwaking, banging on my windows and pooping on my car...