Christians don't believe there's objective morality.

[genkaus]

You are avoiding the issue again, I'm pretty sure you realise that though. Surely nobody thinks that ethics can be grounded in political science or civil engineering.

Quite the reverse actually. Well - not civil engineering, but political science can have roots in ethics.

The economist can tell us what we ought to do to increase productivity but not whether we ought to want to increase productivity for moral ends. The what we ought to do to achieve such and such a goal in the economics case is an instrumental ought, it has nothing to do with morality. The question of whether we ought to want to increase productivity in order to make peoples lives better is a moral ought, but not one the economist can address without appeal to external moral commitments.

Medical science, likewise, can answer questions of what morally ought to be done only once the moral oughts have already crept back in. The premises are not purely factual. Once we agree that something like the limiting of suffering is a moral good, medical science can tell us what we ought to do to achieve it. It can not tell us whether we (morally) ought to limit suffering.

In short: Hume's Is-Ought problem applies to moral oughts, not instrumental oughts.

You are missing the point. The fact is sciences do prescribe "oughts" based on "is" regularly. These sciences do not prescribe moral oughts - nor are they required to do so - because they have little to do with morality.

If science of morality were to become advanced enough to be applied in practice, then there would be no difference between moral oughts and instrumental oughts within its scope. One of the purposes of that science woudl be the discovery and/or establishment of moral oughts.

Now, how can moral oughts (not instrumental oughts) be grounded in a value-free psychology?

Again, that'd depend on the science itself.