The stability is the stability of human nature, and of the objective world which impinges upon what we can decide.

We can in fact switch very rapidly from one set of socially-mandated behaviors to another, and this is a good thing because sometimes one socially-mandated behavior has some significant downside and we should switch.

But the dependence of human life on the earth doesn't change from generation to generation, and the fundamental needs and desires of humans--and therefore how they want to be treated--don't change very much either. Indeed, you see these things across religions precisely because you don't need religion for them. Religion is typically used to help explain and understand such things, but the explanations are kinda all over the place, so if these things are happening for reasons it's just an example of what you say is bad: "using opinion polls to create morality and policy". Maybe some religion would decide that stealing is good and murder is better, and who's to say that's wrong? Only human nature would: people who are stolen from and have their loved ones murdered would, typically, neither stand for this nor agree to call it good.