Out of curiousity, I look at these clerics of Elven deities, and halfling deities and such, do these gods compete for followers?

I mean, would Arvoreen and Yondalla compete for followers, Deep Sashelas and Correllon, Gruumsh and Yurtrus?

This may not be clear, but would <insert racial> clerics try and convert followers of there own race there own deity, pushing worship away from the other god?