Morality is objective and conditional because humans have needs, are capable of suffering, and have some meaningful degrees of agency, both conscious and not. So if you’re a human and you care then there really are objectively correct and incorrect ways to go about the project of caring for yourself and others. You really should do some things and you really shouldn’t do other things. If you care.
The starting place for almost everyone, with limited exceptions for people like psychopaths, is one of emotional investment. This is a function of our numerous interdependencies, evolutionary, political, social, psychological, physiological etc.
Saying that morality can’t be objective because we can’t justify why investment/care is our starting place, is like saying that the practice of medicine can’t be objective because we don’t have a justification for why we should care to save anyone’s life. It’s a premise. It’s conditional, a condition that we all generally meet, and then the practice is objective.
There are plenty of ways to talk about it and even disagree in how we talk about it while still agreeing in practice about the sense in which the relationship between our behavior and the existence of suffering already matters and is consequential.
If you’re someone who doesn’t like to use the moral language of “right” and “wrong” because there aren’t any verifiable/reliable measures of moral behavior from outside of life and thus consider most moral language unfounded, as long as you prefer to avoid unnecessary suffering we are allies in this human project.
Of course I would disagree that categorizing moral sentiment as fundamentally aesthetic means that there are no ways to prioritize or settle disputes between competing moral sentiments. We aren’t so scientifically ignorant of what humans individually and collectively are that we can’t rule out plenty of prescriptions handed down to us from our various religious and spiritual traditions, handed down to us by “God,” as being unjustifiable. We really do know better than to think stoning to death adulterers and those who break the Sabbath etc. is any longer morally or aesthetically preferable or justifiable.
This common human starting point also means that the notion that many raised within religions have that either there is some external metaphysical measure or without it everything is permitted is actually a false dichotomy. It does mean that we can’t rationally/socially expect metaphysical justice, but we do have a foundation for temporal justice.
Of course we can all still have our own individual or group metaphysical intuitions but we can’t expect everyone to share them and we don’t need to.