One reason why some people reject the existence of objective morality is because moral absolutes can conflict.
Canadian philosopher Michael Horner to explains the problem.
He writes:
You may have been confronted with the story of the Nazi soldier coming to the door of the family who are hiding some Jewish people in their home and asking them point blankly, “Are there any Jews here?” The person telling the story then asks you, “What would you say?” or more precisely, “What should you say?”
[…]I think for many people the term moral absolutes connotes ideas like inflexibility and rigidity, and that there can never be exemptions. I have also found that many people believe that holding to moral absolutes means that circumstances are not relevant in a moral evaluation and that moral absolutism cannot handle moral dilemmas. But in fact it is possible to believe in moral absolutes, or as I prefer to call them objective moral values, without adhering to these connotations I have mentioned.
For many people to believe in moral absolutes is to believe in rules that no other rules can ever trump. It follows from this that moral absolutes are all equal and there can never be any exemptions. But what if moral absolutes exist in a hierarchy?
We know from experience that very often more than one moral rule applies to a situation. This often leads to moral dilemmas. So in the ‘hiding the Jews example’ the moral rule of telling the truth seems to apply to the situation, but it would seem that the moral rule to protect innocent human life from torture and murder applies also.
If absolutes are all equal there is no way out of the dilemma. You can’t choose one absolute over another because in doing so you would be violating at least one absolute which, in their view, is supposed to be inviolable.
So, in this case, it seems as if the moral absolutist is stuck in a dilemma. If you lie to save the innocent life, then that would be wrong. But if you tell the truth and hand the innocent person over to murderers, then that would be wrong. Does this really disprove objective moral absolutes?
This problem annoys me, because I know this is the kind of objection to objective morality that annoying philosophy lecturers like to push onto freshmen in order to convince them that morality is nonsense. But does the moral dilemma objection really work?
More Horner:
[…][I]f moral absolutes exist in a hierarchy and the circumstances or the situation were relevant in determining which absolute takes precedent, then there may be a solution to the moral dilemma. That is exactly what I think is the case in the example. I for one have no difficulty knowing that the morally right thing to do in that situation is to protect the life of innocent people from torture and murder rather than tell the truth to a person who has torture and murder in their plans. My moral intuitions are very clear about this.
If someone objects and says, “No, you must always tell the truth. After all it is an absolute, and absolutes by definition can never be violated,” I would point out that they are just using a different hierarchy, putting truth telling above protecting the life of innocent people from torture and murder. There is no way to avoid making a judgment like that since more than one absolute does apply to the situation. I would just ask them to think it through again, and once they see that they have to make a judgment based on some sort of hierarchy in that situation, then I think most people’s moral intuitions will affirm that protecting the lives of innocent people from torture and murder, in that situation, trumps truth telling. There is no way to avoid choosing one over the other.
But isn’t this moral relativism? After all, we are deciding what to do based on the situation! It’s relativism, isn’t it?
No, it isn’t, because there is always one right thing to do in every situation. In every situation, you always follow the weightiest moral rule. The right thing to do does not depend on your subjective state of mind. It is an objective moral duty, and it is the same for everyone, across all times and in all places. That’s what objective morality means -what is right and wrong is not determined by personal preferences or cultural conventions, which vary by time and place.
And of course, God is the ground of this hierarchy of objective moral absolutes. They existed through him before human beings even appeared, as part of his design for us, his creatures. How we ought to behave is grounded ontologically in God’s design for us.
WINTERY KNIGHT 
My personal opinion is that this is part of the the curse of original sin. Having two bad choices does not make one of them good. Choosing between two sins means choosing a sin. My view if sin is that moral laws are like physical laws– it doesn’t matter how you feel. Gravity is gravity — the outcome of a fall from a window is the same whether you jumped, tripped, or were pushed.
Sin is sin. It doesn’t matter is your intent was good. This is the lesson of Uzzah, who touched the ark of the covenant and was killed by God. Some people say that God was upset because of their lack of faith, but there’s no need for that rationalization.
Choosing the sin with the lesser anticipated negative outcome is fine , but it doesn’t remove the sin, or necessarily even make it a lesser sin.
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I look at the objection with another point from the Christian view.
If you recognize that you are confronting wickedness and evil you are not required to play in the moral abuse game. What I mean is that wicked people know when people are moral and hold them to that point, they won’t lie for example. But the wicked lie and do bad things
Basically recognize that discerning the spirits also means knowing when people are doing things not for good but to do purely wicked and evil things.
A Christian won’t help the devil in trying to eliminate good from the world.
And in the case of the Nazi you don’t even need to be that spiritual to know how wicked they were
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Also, Jesus directly asserts the existence of a hierarchy of objective moral duties in Matthew 23:23-24.
The fact that some sins are worse than others (see Matthew Cochran’s analysis at https://matthewcochran.net/blog/?p=2223) also implies the existence of a hierarchy of objective moral duties.
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I agree there are levels of worse. Jesus clearly stated harming kids of high level.
So I use the example of I am against sex outside of marriage. But two adults that aren’t married yet committing the act together is not the same moral issue as harming the young kids as many think is acceptable in this world. It is why the grooming and even abortion ranks on a high scale of wrong before God in my view because it is attacking the young ones that would have come to him is they were given the chance
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God looks at the heart. A man who lies to save the innocent has committed no wrong, just as Rahab lied to save the Israelite spies. One who eats much in celebration is not a glutton because his heart is not set on consuming. One who lies to cover his wrongdoing is another story, as is the true glutton who’s heart is only to satisfy his hunger. Even the act of killing someone is justified by the intent of the heart. Moral relativism is just something people like to argue about, but the absolutes are few and far between. There is no such thing as justifiable adultery or blasphemy or idol worship, so the lying thing is just something to create argument.
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