DNA does change. There are "point mutations", for example, in which say a single nucleotide changes, say from guanine to cytosine. . . . CTG TCA . . . becomes . . . CTG GCA . . . If there is a strand of DNA that suffers such a change, is it then not the same strand of DNA? This is exactly like the question whether persons become different persons if they lose say half a finger. And now we have the problem of DNA identity. When are two descriptions sufficiently similar to count as descriptions of the same strand of DNA? Anthony Quinton has the general issue right, in a 1962 article in the Journal of Philosophy called "The Soul": 'No general account of the identity of a kind of individual thing can be given which finds that identity in the presence of another individual thing within it. For the question immediately arises, how is the identity through time of the identifier to be established? It, like the thing it is supposed to identify, can present itself at any one time only as it is at that time. However alike its temporally separate phases may be, they still require to be identified as parts of the same, continuing thing.' By the way, 6% of identical twins do not have identical DNA, so the members some pairs of identical twins would be metaphysically identical and some would not.
This question is at the extreme end of a cloud of questions. The person who picked up your stray hair might use your entire genetic information (cloning) or any subset thereof. I don't think there is a general moral answer here about where to draw the line. There are some clues to a moral answer about how the line should be drawn in the law.
Obviously, the less of your genetic information is copied, the less of a legitimate interest you have in preventing the copying. If they just copied the bit that controls hair color (I know, this isn't quite the way it works, but let me simplify a bit), then it is hard to see how you would become worse off by the fact that there is someone somewhere 20 years younger than you who has the same hair color.
In cases where more substantial chunks or your genetic information are copied, you may well become worse off -- for example, because your talents, looks, or basic personality traits become less unique. In these cases, the more copies are produced, the stronger your grounds to object.
Whether these grounds can be outweighed depends on the purpose and context of the genetic engineering. Suppose that, thanks to a rare combination of genetic traits, you have immunity against a nasty communicable disease. It's highly desirable that many in the next generation have such immunity. In such a case, the interest of society might outweigh your interest in preventing that, thanks to the use of your genetic information, many in the next generation are uncomfortably similar to you.
There's ample space for reasonable disagreement about how to weigh the competing interests here, and the decision should ultimately (once we get there, technologically, and thus have a better understanding of what is and is not technically feasable) be made by an elected legislature -- differently, presumably, in different jurisdictions. Such legislatures may also need to decide two further matters:
(1) who is allowed to extract and store genetic information, and for what purposes and with what safeguards (there are probably good reasons to make it illegal for any old hobby geneticist to collect stray hairs from people and to extract and store their full genetic information); and
(2) whether there should be (tradable or untradable) private property rights over genetic information and, if so, how these should be conceived.
While there is no good case for saying that persons have a natural right to veto the use of their genetic information, there are good reasons to be cautious in regard to legalizing -- especially commercial -- use of genetic information, even with the consent of the person whose genetic information it is.
Just to clarify terminology. I would understand an empirical theory of ethics as one that explains the activities of a group of ethicists. An empirical theory of descriptive ethics would seek to explain the activities of those who describe ethical beliefs and practices; and an empirical theory of normative ethics would seek to explain the activities of those who justify or challenge ethical beliefs and practices. An empirical theory of normative ethics would not itself seek to justify or challenge normative-ethical propositions.
Leaving terminology aside, I think what you mean to ask is whether an empirical account of how human beings behave has normative implications. In response, I would certainly agree that it does not follow from the fact that human beings tend to behave in certain ways that they ought to do so. Still, I would not think that empirical knowledge about human beings is normatively irrelevant. Two examples. If a morality is too complicated for human beings to understand or to follow with reasonably accuracy, then we might conclude that it is not the morality that human beings ought to try to follow. Similarly, if a morality is so demanding that we do not manage to educate most human beings to follow it, then again we would seem to have reason to conclude that it is not the morality human beings ought to try to follow. I see morality as solving the practical task of helping us live together peacefully and in a way that lets us flourish individually and collectively. On this account, we should be sensitive to empirical information and practical experience.
Should you be interested in more on this question, you might want to look at my exchange on this with Jerry Cohen (who takes the opposite view to mine). My response to his book -- Rescuing Justice and Equality -- is "Cohen to the Rescue!" in Ratio 21/4 (2008), pp. 454-75.
As happens often, also with professional philosophers, your word "then" marks the weakest spot in your argument. "Our instincts that say we should behave in certain ways are merely adaptations that increased survival. It seems then that there is no objective answer to 'What should I do?'."
How does the second sentence derive support from the first?
Our instincts may predispose us to get frightened by certain sights and sounds, and we may through evolutionary factors have become disposed to overestimate vertical distances and to underestimate horizontal distances over water. Does it follow that there is no objective answer to the question of whether those sights and sounds really are associated with danger -- no objective answer as to what these distances really are?
I think your worry comes about as follows. You believe that what really goes on in moral philosophy is that people are "looking for a consistent framework for decision-making that best coheres with our moral intuitions (which arose because they increased survival)." You then say -- quite reasonably -- that the successful construction of such a consistent framework cannot count as the discovery of objective morality.
Why not? Here you might give two answers. One answer says that what our instincts dispose us to do is often wrong (e.g. when young males feel strongly inclined to take advantage of a safe opportunity to rape a female). But this answer would seem to presuppose rather than deny that there is an objective morality. Moreover, the fact that this answer is widely shared among moral philosophers shows that they do not count whatever our instincts urge us to do as a moral intuition. Our instincts may urge us to save ourselves from a dangerous situation, which we caused by our own negligence, through an action that is likely to kill innocent bystanders. But our moral intuitions tell us that this would be quite wrong.
The other answer says that history might have gone differently and might then have produced different instincts and moral intuitions. But since there can only be one objective morality, the moral intuitions that emerged in this history we actually happened to have cannot be a good path to discovering what this objective morality is. This answer makes some sense but, to reach your conclusion, you need to overcome two further hurdles. First, why cannot the morality that best accords with our moral intuitions be objectively right for our world even while another morality would have been objectively right if a very different history had shaped our moral intuitions differently? Second, are moral intuitions really the only basis on which an objective account of morality can possibly be established?