On theism, why do humans have moral duties even if there are objective moral values?

[Angrboda]

The primary answers given were a) doing good is rewarding in itself (both natively...

Theism isn't necessary for that. That's why I don't find that a useful reply.  

... and because God has made it so [Angrboda, Mister Agenda])

Do you mean God has made the rules that doing good would result in reward in the afterlife? The last part of my question was "other than for a selfish interest in going to heaven or avoiding hell". "God has made it so" (if it means doing good would result in divine reward) seems to be about god's reward and punishment as a motivation for theists to do good, which is something my question wasn't/isn't looking for in an answer.

Secular science does not acknowledge God's law being intrinsic to human nature. If God has made his law intrinsic to human nature, He has made doing good intrinsically rewarding. So, no, you simply didn't understand the answer. It has nothing to do with self-interest. God has made it so by making us as we are; similar to Natural law, but with explicit biblical support. And I have to ask, what part of "rewarding in itself" did you not understand? Speaking of destroying your logical faculties, separating a compound clause and treating them as independent clauses doesn't speak highly of your faculties. This is nothing but a reading comprehension fail. I might excuse it except for the fact that I'm sure your native tongue has the same rules for compound clauses as English.