The research Everett and his colleague report suggest a different way of thinking about moral reasoning. Flexible morality may be a better guide to making difficult decisions in a complex world. But if you want other people to trust and cooperate with you, it’s better to let them know your moral values are absolute.
https://www.psychologytoday.com/us/blog/talking-apes/201611/where-does-our-moral-sense-come
I'm more of a morally flexible guy, still generally people see me as trustworthy. Usually I don't discuss my morals with most people so I imagine they assume a lot.
But when it comes to moral judgments like these, most of us aren’t swayed by argumentation. Our innate moral sense is absolute. It allows no exceptions, regardless of extenuating circumstances. Yet why should this be? Throughout history, humans have repeatedly faced situations in which they had to violate their innate moral code. They kill attackers to save themselves or family members. They lie so as not to hurt the feelings of loved ones. It seems that a flexible moral sense would be more adaptive.
In a recent paper, University of Oxford psychologist Jim Everett and his colleagues laid out a theory to explain the rigidity of our innate moral sense. They propose that our intuitive morality has been shaped not by the day-to-day dilemmas we face but rather by the opinions of other people. More specifically, Everett and his colleagues hypothesize that statements and behaviors consistent with an absolute moral code are signals of trustworthiness.
This is what I've generally assumed, that there is a genetic factor . . .
It seems you've already gotten into the this matter, but I didn't really see where it began.
In any case, there is nothing in what you quoted that says anything about "a genetic factor". And I don't understand from what fact one might draw a conclusion about "a genetic factor" being relevant to the issue of moral precepts among humans. After all, being a mass murderer and then producing and raising children would presumably be an effective way to differentially increase the frequency of one's genes in a population. But that does not suggest in any way that mass murdering is a moral act.
Anyway, I find it difficult to answer the questions you've asked about "flexibility," in the first place, depending on what is meant by "flexible". Additionally, every response I think of depends on what level of generality one is referring to. For instance, I have no difficulty saying (something like) that it is always immoral for a person to intentionally harm another sentient creature merely for his/her own pleasure. But there could presumably be lots of discussion and dispute about what is meant by the terms "intentional," "harm," "sentient" and "his/her own pleasure". Depending on what those terms mean, it seems conceivable that there could be some specific act that could fall under the purview of the stated precept that might be not immoral--although, I can't think of any such instance or definitions offhand.