It would have to use the scientific method to develop a transparent set of social agreements about basic moral principles – whatever we agree those most basic of moral principles to be – instead of on the assumptions of natural moral facts (as there are no such things). To the non-philosopher, this translates as reducing the moral principles we wish our societies to be guided by to the most basic sets they can possibly be – however we wish this to look – and then using reason and science to build consistent moral rules, and make consistent moral decisions based on these most basic of principles. For example, we might look at our current principles about murder/violent crime and then reduce them to a basic principle that suffering and death should be avoided wherever possible. From there we would judge whether our laws were rationally consistent with what we socially agreed.
All be it a very different type of science, moral science can exist in a socially created space like this without contravening the rules of rationality, all the while allowing the most important of humanities problems to be exposed to the fruits of scientific method. Indeed, most areas of politics and morality need not be thought of as subjective at all once moral science is on the table, unless the problem is wholly without reason or evidence on either side. This doesn’t mean opponents of rationality will suddenly drop their beliefs and join us, but it does provide a consistent framework to stop people having to turn to religion or other methods in order to form moral beliefs. We shouldn’t underestimate the secular advantage this would have in future generations.
Moral science is important: it’s more rational than what we currently have, ie, a system where we just slightly amend historically decided ideas when we really have to. But more than this, it’s important because it gives us a chance to rationally judge moral issues – no longer having to allow for dangerous and often irrational subjective differences. What’s more, it allows for the whole method to be scientific in attitude; not allowing for certainty where there is none and helping to do away with as much potential for uncompromising aggression as possible.