Neil Shenvi has a website where he argues for one interpretation of "good" and "bad," which is that these words describe something objective -- something that's true independent of the beliefs of humans. He says that "moral facts" exist (in philosophy, this qualifies him as a "moral realist"), and he gives what he sees as evidence for their existence. (While Neil is a Christian, his evidence is not based in Christianity. So, I'll not need to respond to anything uniquely Christian, or even theistic.)
The first piece of evidence is that "Nearly universally across human cultures, there exist the same basic standards of morality."
My first response is to question how true this statement is. Sure, there are certain morals that most cultures agree upon presently and even throughout history. For example, killing somebody for no reason is, and may have always been, considered to be wrong. However, there are other morals issues that cultures have disagreed upon. For example, capital punishment is disagreed upon. So, while killing is generally viewed as wrong, it's often disagreed upon regarding when killing may be permissible. I think this could be said for pretty much all the popular moral issues, like lying, stealing, raping, etc. While they are generally viewed as wrong, they are disagreed upon over when it may be OK to do these things. So, I'm saying that while there is significant agreement over certain morals, there's also significant disagreement.
(before I continue, I just want to note that even if his statement is true, and it may very well be, I'm not sure how this would be evidence for "objective good" and "objective evil", but more on that at a later time.)
Now, Neil could respond by saying that, while there is significant moral disagreement throughout cultures, there's also significant disagreement among scientists over the nature of the external universe, and that doesn't mean the external universe doesn't exist (objectively). Further, Neil could say that even considering scientists' views on the external universe have changed over time (like cultures' views on morality have changed over time), that doesn't mean the external universe doesn't exist, and therefore, neither do objective morals not exist. Well, to me, comparing the existence of objective moral values to the existence of the objective universe is not a good comparison.
Take a wooden chair, for example (which is part of the objective, external universe). We can test the chair, examine it scientifically, compare it to other chairs, see how it reacts in different environments, repeat all of our tests and see how consistently we get the same results, and so forth. The chair can be observed in many ways that do not rely on our opinions alone, thus showing that the chair most likely objectively exists. (This is why scientists generally don't disagree over the existence of the external universe, only it's nature.) However, we cannot perform these tests on "objective good". It is not an object. It has no material existence for us to test, and so it is not comparable to the external universe.
However, it could be argued that the objective, external universe does not consist solely of material objects, but also abstract objects, and, like morality, these abstract objects exist objectively. For example, numbers are said (by some philosophers) to be abstract objects that exist objectively (i.e. independent of human opinion). To that, I would respond with questioning the objective existence of numbers.
To what extent do numbers really exist objectively? Sure, numbers can be used to refer to material objects -- like, to describe things. For example, there is "one" chair. But to what extent does the number "one" exist without the chair?
Neil might agree, and say that "one" does not exist without the chair, just like "objective morality" wouldn't exist without that to which "objective morality" refers! To that, I would ask, "to what does 'objective morality' refer?" If it's something material, then we could compare it to the external universe -- and it would be something we could test. But if it's something abstract, then I would question that thing's existence, as well.
On the other hand, Neil might disagree and say that "one" does exist without the chair. For example, it exist in our minds. However, but that's not objective, but rather subjective. So, it seems that numbers, apart from the material things to which they refer, may not objectively exist. (Now, I'm far from a philosopher or theoretical mathematician, or whoever would be an expert in these questions about the objective existence of numbers, but I'd be interested in knowing if I'm wrong about all this).
So, while there is significant agreement about morality throughout cultures, there's also significant disagreement. And while there is disagreement among scientists about the nature of the external universe, and this disagreement doesn't threaten the objective existence of it, the existence of the external universe cannot be compared to the existence of objective morality.