My sense is that you are referring to a form of relativism that takes the specific form of morality by convention. Or at least that the social attitude you describe can be set out in these terms. It is capable of development beyond the banalities of prevailing forms of relativism. I develop this below, just slightly, but it may be that this is not at all your angle of interest. If it isn't, excuse the misunderstanding.
A version of this form of relativism can be found in FH Bradley's Ethical Studies, ch. V, 1876, in JN Findlay's 'Morality by Convention' (1944) and (at a stretch) in Wittgenstein's conception of 'forms of life' in Philosophical Investigations (1953, rev. 1958).
The central idea is that only in the context of a set of institutions, customs, and practices - a set of conventions - can moral obligations, duties, and rights arise. These institutions, customs, and practices are historically and socially specific; and since moral obligations, duties, and rights are indexed to them and vary with them, 'morality by convention', just described, is a form of relativism.
I am mainly trying to explain the idea of morality by convention, and not to defend it. But there is some substance to it. If you think of the morality of the English medieval manor, moral obligations, duties, and rights all stemmed from the institutions, customs, and practices of the time. The manorial rights of property-holding, for instance, were sustained by institutions, customs, and practices of the manor, and vanished when the social structure of the manor passed away.
An important point to note is that morality by convention is prescriptive, not merely descriptive. On this view of morality, moral obligations, duties, and rights are all actually binding - objectively binding. They are, if you care to put it so, emergent properties of the social structure. To outline them is not to do the sociology of morals, or merely to characterise popular morality. It is to specify real moral requirements, objectively binding on the community, but real moral requirements that are also relative to a specific social structure.
The oddity or distinctiveness of this idea - I use the terms neutrally - is not to be under-rated. We are all familiar with various forms of relativism, the burden of which is that there is no such thing as an objective morality - only moral diversity. Morality by convention takes us by surprise. It combines relativism and objectivity. On the other side, just as it interlocks relativism and objectivity, so also it breaks with the idea of a universal objective morality. Objective morality exists, all right, but in forms that are historically and socially specific and that need never converge in a single moral code.
J.N. Findlay, 'Morality by Convention', Mind, Vol. 53, No. 210 (Apr., 1944), pp. 142-169.
F.H. Bradley, Ethical Studies, 1876 and regularly reprinted.
L. Wittgenstein, Philosophical Investigations (1953, rev. 1958), paras. 241-2 et passim. See further : https://nb.vse.cz/kfil/elogos/history/24_02_tonner.pdf.