The Big Two possessed a mixed relationship with religion. A huge chunk of humanity earnestly believed in something greater.
The Mech Trade Association frequently grappled with religion due to their recruitment policies. If they wanted to recruit promising mech pilots, mech designers and other capable people, they couldn't afford to snub the religious side of humanity.
As the self-proclaimed protectors of humanity, they derived their legitimacy from how their internal members partially reflected the people they protected. If they completely eschewed believers in their ranks, religious states across human space would rebel at being ruled by overbearing secularists!
While the Common Fleet Alliance suffered less from this problem, they too had to take religion into account as many powerful spaceborn clans believed in space gods and the like!
