But the fact that someone could make that religion doesn't make this religion any less valid.
No, what makes it not a religion is the fact that it's not really a religion. It's a political ideology. A philosophical discussion group. A guild. A knightly order. A drinking society, even. But it is not an organization intended to venerate, worship, promote, idolize, or in any other way spread the influence of the gods
they worship. In fact, it is almost the exact opposite. It is that fact that, in my interpretation of the intentions of the mechanics of the game, make it not a religion in the sense of BattleMaster game mechanics.