Is morality objective or subjective (relative)?
To answer this we have to be specific about what the question means. When I perceive a property of a thing, that property could be in the thing itself, or it could be an attribute that is "painted on the thing" by my mind.
For example, I might say that a particular building has many properties including these two: it is 100 feet in height, and it is tall. If I were from rural Kansas, any building over 50 feet in height would be tall to me. However, if I were from the city of Chicago, a building would have to be over 500 feet in height for me to consider it to be tall. So it is quite obvious that my personal history determines what is tall, whereas height is unambiguous, no matter where I come from. Height is objective, but tallness is a property my mind subjectively paints onto objects with height.
Now, there are two ways I can establish the objective/subjective nature of an attribute. I can positively show that an attribute is objective by finding evidence that the attribute is independent of subjectivity, or I can positively show that the attribute is a subjective property generated when a mind sees objective attributes of other things.
In the case of tallness, we certainly have positive evidence that tallness depends on where you come from and what experiences you have had. We can predict that anyone who has not seen a building more than one story tall will think that the Empire State Building is very tall.
But what would be considered positive evidence of objectivity?
I realized last night that subjective attributes are invisible to non-thinking entities.
Suppose I hold a conical projectile in my hand. The projectile is 10 centimeters long and has a mass of 1 kilogram. I fire it at a metal plate, and the way the plate behaves upon impact depends upon the mass. Yet the plate has no subjectivities of its own because it cannot think. If the mass were a subjective attribute painted on the projectile by my mind (e.g., say, if all 10cm conical objects subjectively feel like they are 1 kilo masses), then why should an inanimate target care about my subjectivities?
One might suggest that the apparent attributes of the debris are also subjective inventions, and that is why they appear correlated. However, this would be rather a coincidence. And we can establish increasingly complicated experiments that will force us to argue for increasingly bizarre coincidences should we stick to the idea that mass is subjective. Thus, we have to give up the idea that mass is a subjective quantity.
Furthermore, we can devise ways to hide from us every attribute of a projectile except for its mass. In that case, it cannot be that mass is some subjective mental decoration we apply to objects with other objective attributes (like size, shape or color).
Yet, with morality, there is no similar evidence of objectivity.
There is no way to create a curtain through which only 'evil' passes. If we could do so, we would have strong positive evidence that evil was objective and not some invention of our minds.
Also, there's no evidence that good and evil affect the environment. If an evil act occurs, it leaves no trace on non-thinking entities. A barrel of oil that was stolen burns as long and as brightly as a barrel of oil that was fairly obtained.
While there may be theories of morality (e.g., the Golden Rule), these theories predict nothing but our own subjective feelings and tendencies. They are not like objective physical theories that predict the behavior of non-mental entities. Rather, moral theories predict the behavior of mental entities that have subjectivities.
In addition to this lack of evidence for the objectivity of morality, there is a growing mountain of positive evidence for the psychological and evolutionary nature of moral perception.