To use a real world analogy (which I am loathe to do, as worship in-game is a whole 'nother ball of wax, but hey), if I am a fanatic Catholic, I might respect the work of a fanatic Protestant, I might even share a church (as they do in the show, The Gilmore Girls, where a small town has one church for two congregations), work together on common goals, hold get-togethers and fundraisers together - but it would certainly affect me if a member of my congregation switched and became a Protestant instead. I would be glad that they didn't become a Satan-worshipper, but I would not be happy.
How much stronger would this feeling be in a world where Protestants would literally support another god, and would give real and tangible power to that god (and away from my own) by becoming a worshipper?
What would even be the point in-game of having two separate gods if it didn't matter to the players, or to the gods themselves, which was worshipped?
I don't see either the sense or the advantage to it - but for those of you who do, feel free to tell me what I am overlooking.