But this question is very sound: after some reflection, it makes sense to me that Eberron is a world full of exceptions and contradictions and grey areas.
If my human cleric wants to worship the Lord of Blades against all social norms, or my dwarf wants to become one of the Deathless after being an ambassador to the elves for some time... why not?
It totes makes sense to me that some abilities will be strengthened by their favored race, i.e. the Undying Call ability working as True Res rather than Raise Dead for elves.
I think that following the general theme of Eberron would allow non-favored races to worship any gods they'd like, and may the strongest prevail.