Moral frameworks are neither objective, nor subjective
(The flair is to highlight the fact that I am talking out of my ass here.)
I've quit thinking of moral frameworks as either objective or subjective. This happened when I realized moral frameworks are imposed. The difference is the source of the framework, and in what the framework is rooted.
For many, like Christians, the imposition is through a religious tradition, rooted in a god-concept. For others, the imposition is secular, rooted in the state. And still others, the imposition is natural, rooted in human empathy. There are probably more that I don't know about.
We might call these subjective or relative, but that's as inaccurate as calling them objective.
I guess the next question is, how do you judge which is best? For now, I'll leave that to the philosophical thinkers, as I've just started thinking about morality this way. Maybe I'll find a method for judging one over another. Or maybe they're all equal. Or maybe it's turtles all the way down.