Chaos and order are intrinsic in the universe. There is no morality. That is a construct of a chaos-prone and fallible species that arrogantly presumes to be in charge, the whole while making our planet potentially a hostile and unlivable place for said species... and all others that haven't yet been wiped out by... well, US.
Assuming "intelligent" life is not just a horrible aberration to universal order, then it stands to reason that one of two outcomes will prevail:
We will figure out how to live in harmony with the world and universe around us... perhaps this will be like Gene Roddenberry's vision of societal collapse and utopic resurrection. *shrugs Or not. *shrugs again
We will cease. The planet will continue until it, too, ceases when the sun expands and swallows up the inner solar system.
As to how we live our lives as humans on this rock, together, yet disparate (even though we are not?)...
I see the need for a massive paradigm shift in what it means to be alive, and human, and oh so very fragile. We need to stop turning inwards as we are wont to do (even in the face of globalization... or especially in the face of...). We need to stop celebrating our differences for the sake of being different.
Yes, that list can go on. But to what end?
Morality is an imposition of order onto chaos; a means of control.
The OP wanted to remove the politics that his question was framed by. But politics and religion are what have defined morality from the earliest days of any organized civilization.
Maybe instead of asking how does morality change, we should seek to answer how to change morality?
If morality, as I suggest, is a means of control, then who is determining the method of control and placing the yoke upon the rest of us?