what do you think of this statement from that same Book:

"If morality is culturally relative, it does not follow that we should not interfere with the customs of other cultures; what follows is that we should interfere with other cultures if doing so accords with our customs."

It is perhaps then unsurprising that some should have concluded that, where such rival moral standpoints are concerned, all fundamental rational justification can only be internal to, and relative to the standards of, each particular standpoint. From this it is sometimes further and at first sight plausibly inferred that this is an area of judgement in which no claims to truth can be sustained and that a rational person therefore could, at least qua rational person, be equally at home within the modes of life informed by the moral schemes of each of these standpoints. But this is a mistake. ...

The protagonists of those standpoints which generate large and systematic disagreements, like the members of the moral communities of humankind in general, are never themselves relativists. And consequently they could not consistently allow that the rational justification of their own positions is merely relative to some local scheme of justification. Their claims are a kind of which require unqualified justification. ...

What is being claimed on behalf of each particular moral standpoint in its conflicts with its rivals is that its distinctive account (whether fully explicit or partially implicit) of the nature, status and content of morality (both of how the concepts of a good, a virtue, a duty and right action are to be correctly understood, and of what in fact are goods or the good, virtues, duties and types of right action) is true.

Two aspects of this claim to truth are important to note at the outset. The first is that those who claim truth for the central theses of their own moral standpoint are thereby also committed to a set of theses about rational justification. For they are bound to hold that the arguments advanced in support of rival and incompatible sets of theses are unsound, not that they merely fail relative to this or that set of standards, but that either their premises are false or their inferences invalid. But insofar as the claim to truth also involves this further claim, it commits those who uphold it to a non-relativist conception of rational justification, to a belief that there must be somehow or other adequate standards of rational justification, which are not the standards internal to this or that standpoint, but are the standards of rational justification as such.

Secondly, just because this is so, making a claim to truth opens up the possibility that the claim may fail, and that the outcome of an enquiry initially designed to vindicate that claim may result instead in a conclusion that the central moral theses of those who initiated the enquiry are false. One might have concluded from the account of the fundamental disagreements between rival standpoints which relativists have taken to warrant their conclusions that, just because the standards to which the partisans of each appeal are to a significant degree internal to each standpoint, any possibility of something that could be recognized as a refutation of one's own standpoint by that of another was precluded. Since each contending party recognizes only judgements by its own standards, each seemed to be assured of judgements only in its favour, at least on central issues. But when one notices that the claim made by each contending party is a claim to truth, this inference is put in question. ...

What the claim to truth denies is, as Nietzsche understood, any version of perspectivism. ...

Yet if the claims made from the rival and contending points of view are not claims to truth, the adherents of the different standpoints in contention will not be able to understand the central claims of their own particular standpoint as logically incompatible with the claims of those rivals. ... It is only insofar as the claims of any one such tradition are framed in terms of a conception of truth which is more and other than that of some conception of rational acceptability or justification that rival moral standpoints can be understood as logically incompatible. ...

The exercise of this imaginative ability to understand one's own fundamental moral positions from some external and alien point of view is then yet another characteristic necessary for those engaged in enquiry who, beginning within some one particular moral standpoint, aspire first to identify and then to overcome its limitations. What this ability can on occasion achieve is a discovery that problems and difficulties, incoherencies and resourcelessnesses, in dealing with which over some extended period one's own standpoint has proved sterile, can in fact be understood and explained from some other rival point of view as precisely the types of difficulty and problem which would be engendered by the particular local partialities and one-sidedness of one's own tradition. If that alternative rival point of view has not proved similarly sterile in relation to its own difficulties and problems, then the enquirer has excellent reasons for treating the alternative rival point of view as more powerful in providing resources for moving rationally from a statement of how things seem to be from a particular local point of view to how they in fact are, by revealing what it was that was hitherto limiting in that standpoint which had up till now been her or his own.

So even though all such reasoning has to begin from and initially accept the limitations and constraints of some particular moral standpoint, the resources provided by an adequate conception of truth, by logic and by the exercise of philosophical and moral imagination are on occasion sufficient to enable enquiry to identify and to transcend what in those limitations and constraints hinders enquiry or renders it sterile. ...

So on fundamental matters, moral or philosophical, the existence of continuing disagreement, even between highly intelligent people, should not lead us to suppose that there are not adequate resources available for the rational resolution of such disagreement.

systems of traditional, moral rules are not like the axioms of, say, set theory ("a point never understood by naive rationalists like Rand" apparently).  What we have rather are rules which, in some cases, contradict each other. But these are part of a larger system in which context and other rules suggest where one rule is to prevail over another.

This is why genuine moral conflict can amount to a clash of one good over another.

Further, this is not something concocted by intellectuals. It's not an ethical theory. It's rather an empirical fact about the moral dimension of human society.

Politicians are alien reptiles who feed on human flesh.
As anyone can see with their own eyes, politicians slither around questions like they are snakes or something -- always managing to avoid being pinned down. Also, they, at least metaphorically, "bite" at their opponents with negative campaign ads.
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Further, this is not something concocted by intellectuals. It's not political theory. It's rather an empirical fact about the political dimension of public society.