You can call it anything you want, but by your denying its objective correctness you tell me all I need to know about what this “morality” is, and more importantly: what it fails to be. It is really nothing more than “might makes right” and that if the Nazi’s had won WW2 and prevailed in spreading their cultural preferences around the world, then maybe it would be considered okay right now to exterminate any remaining Jews that anybody finds.
I prefer real morality [notice my own careless lapse right there! – it really doesn’t matter what I or society prefers] … the sort that can speak truth to power even if the entire world under the sway of that power tries to deny it. Subjective “morality” provides no basis for speaking truth to overwhelming power. It just has to shrug its shoulders and declare that “this is the new right thing to do now.” It makes incoherent shambles of your own attempts to criticize old testament atrocities because your cultural preferences today carry no more weight than their own did back then. But your willingness (a very healthy and necessary willingness, that!) to join with Christians in being horrified at atrocities of the past (as well as in the present!) is evidence of a healthy moral framework that you’ve imbibed from somewhere – it certainly didn’t come from any logic or reason or science as those have exactly and precisely zero to contribute in support.
Logic and reason provide the methods and rules for how to construct a valid argument. But it needs premises to work with. Now some premises might themselves be products of prior reason, such as when a system of mathematics is built up on prior proven theorems. But it all works back to some axiomatic set which is a foundation for holding up the whole edifice. Without premises, there is nothing for logic or reason to work with. And some of these premises (the ultimate ones – the postulates) must be from outside the whole set, themselves only accepted – not established by the system itself. No system is self-sufficient and complete in this regard. Godel proved something similar about mathematics, and if it’s true for math (the only real home for what we can justifiably call ‘proof’), then it’s a pretty safe bet it’s true of less logically rigorous systems (such as science) too.