Both.
It depends on what you mean by morality.
If you use wellbeing as the basis for morality, then the basis for morality is objective. The application of that then becomes subjective.

Turns out it's both

Subjective, as it seems, like everything else it evolves and changes over time. It changes in a way similar to natural selection. I think there are objective things that help our species or don't. Morality itself isn't objective because the universe doesn't "care" about what we do or not. It is up to us as a species to get things to where we think we need to be at, as to how we best interact with society as a whole. This really can't be enforced outside of law but suggested through education and interaction. The reasons for our actions may have a chemical reason as well, but morality itself isn't objectively floating around in space or something.

I'm voting for both: objective as a set of biological/genetic/epigenetic adaptations, and subjective in that the impulse created by the adaptive traits manifests through the feelings/emotions. Shame, disgust, altruism, justice, love, etc.

As OB1 would say it s a matter of perspective.

The establishment of the basis for a moral ode is subjective, but it can establish objective standards. Comparison of a decision or action to an objective standard can and should be as objective as possible. We can never remove all subjectivity.