The point of this OP is to discuss what exactly constitutes a morally informed law, and perhaps more generally, what it means to base law on established moral principles/rules/heuristics/etc. I am mostly looking to get a sense of what the relationship between these terms and concepts is; I am not making the argument that morality should inform our laws much, or even at all, at this point.

It seems to me that any substantive morality that actually makes meaningful statements about right and wrong, not just that good amounts to “evolutionarily advantageous developments arising from eusocial primates attempting to thrive”, and bad is “not useful”, can translate quite neatly into law - but so can relativism and the view that morality is just a set of useful constructs.

But are the latter really morally informed, or are they informed by something subjective and something that could only be justified if useful, respectively? If you define morality as “a set of useful constructs” the laws informed by it make no claims about right and wrong; furthermore, the claim that useful constructs should be considered for moral status is self-defeating because under this paradigm it could only be supported by another - merely useful - construct, and to make a law based on a relative attribute - such as intelligence - is to defeat the purpose of the justness of laws that can be reasonably expected to be just, which, while not absolutely necessary, is recognized to be highly desirable.

So, it seems to me that the only truly morally informed laws that exist are the ones that are informed by a morality that:

1) Accepts that moral propositions exist
2) Is sufficiently confident to make some basic universalized claims
3) Is at least somewhat sensible even in the absence of total knowledge of the morality informing the law or independent of the status of the morality informing the law

(1) and (2) are merely stipulated because moral constructivism (or whatever you want to call it) and moral relativism fail - as usual.

(3) is where it gets interesting. If we had a morality that we suspected might be correct but could not understand due to missing bits or was so volatile that its applications could not be parsed, then we have a poor contender for something to inform our law, as law is by definition an application of theoretical knowledge, and if that knowledge cannot be applied, it is useless in this context. A contender would be some ridiculous utilitarian decision-theory-based calculus.

This is all without running through the different moralities that we could use to inform law and how they would differ, but the conditions I outlined I think are necessary, although perhaps not sufficient, to designate a morality that can inform law.

You may notice that I still haven't specifically said what a morally informed law is, but rather a morality that could inform a law. That is intentional; I still don't know how to define what a morally informed law is, as the process of creating a morality that can inform law is somewhat trivial according to the outline, so a morally informed law could be anything from "wrestlers are despicable and must be crushed" to "bananas are the highest order fruit and must only be enjoyed peeled".