It is not a disdain for sociology - I quite like the field - I just don't think what they do is really scientific. While they purport to use scientific method conceptually, it is only in the very loose sense you described. The nature of the field is such that it cannot use maths to make proofs. The best it can do is collect empirical data samples (usually small due to lack of funding) that usually have poor variable control and conduct statistical analysis to make some conclusions. It is far from giving the same level of certainty in its claims as physics or chemistry - while even those do not give 100% certainty, we can send people to the moon with them. I can't say the same for sociology.

As to your second point, why something 'is' in a scientific sense is because something else 'is'. It is the examination of why in a causal sense. Apples fall from trees because gravity exists. It is not because things ought to be that way or because apples have some moral trait. That is no longer the realm of science.

Science can tell us whether humans feel positive or negative emotion from certain stimuli. That is an 'is' proposition. Science however cannot tell us how to create a moral framework UNLESS we take the starting step and say something like 'any moral framework must maximise the positive emotions felt by the people in it'. And at that point, we have pulled an ought statement from absolutely nowhere!

Regarding the paradox - you have described the 'is' / 'ought' problem outlined by Hume and the limit of how much science can intrude on philosophy. Real scientific facts can cause us to consider new moral questions - developments in technology commonly do this. But they do not automatically create moral predicaments. That requires someone to think about whether a situation is moral (unless youre an objectivist).

Science can give us new options in responding to moral questions. It can create situations that are themselves new moral questions. But it cannot answer those questions for us by itself. Science in a pure sense is amoral.

This is precisely what I am contesting - the proposition that science is the measure of all things is not itself a scientific proposition.

As for sociology, I would hardly describe it as science itself, but even if I did bite on that one, I would say sociology is concerned with what 'is' - it can make claims about how human societies develop and organize themselves and so forth. But as soon as you delve into the question of how a society ought to organize itself, you have (at the very least) a couple of choices:

1. You could go into political philosophy (ie. not science); or
2. you could make the normative and unscientific claim that societies ought to organize themselves by reference to past behaviour that sociologists have uncovered or have claimed is more beneficial to human happiness/existence etc (which of itself is another normative and unscientific rabbithole that broadly smacks of utilitarianism for the most part - another unscientific moral framework).

But regardless of which choice you make, in the end analysis, you are not making recommendations on the basis of science - you are either making a moral determination to defer decision making to science by reference to what is likely a utilitarian framework (and then science just fills in the blanks) or you are properly considering moral questions in the realm of philosophy and not simply ignoring that trusting science with moral questions is of itself a moral judgment.

What scientific claim supports the starting proposition that 'morality is aimed at protecting human interests'?

What scientific claim supports that determining human interests is a scientific endeavour?

It seems Shermer is taking normative 'ought' propositions without acknowledging them or dressing them up as scientific 'is' propositions and then using those propositions to further propose that science OUGHT to resolve moral issues.

And I cannot lie.