It is considered in bad taste to bring God into contemporary bioethics discussions. Why? Well, one reason is that if one does so, one's argument will be irrelevant to atheists and agnostics. But note that in the American public, the percentage of people who accept the existence of God is significantly greater than the percentage who are Kantians, or utilitarians, or virtue ethicists, etc. Thus, say, an argument in favor of cloning based mainly on the premise that God exists (I don't know of any such argument off-hand) will be relevant to a much greater percentage of people than an argument for the same conclusion based on Kantianism. Moreover, while among academics there are significantly more atheists and agnostics, it still may be that the claim that God exists is at least as widespread as a belief in Kantianism, or in utilitarianism, or in virtue ethics.
Another reason it's in bad taste is that it allegedly brings faith into what should be a reasoned discussion. But this presupposes that the existence of God cannot be argued for rationally, a claim that is false (clearly false if we use as our standard of rationality the level of compellingness of arguments in applied ethics). Now one might with greater plausibility claim that no argument for the existence of God will be compelling to all, or even to a majority, of intellectuals. But it is in perfectly good taste to give serious bioethics arguments based on premises that are not compelling to the majority of intellectuals. Thus, one can give Kantian, utilitarian or virtue ethics arguments.
A third, though very pragmatic (but so is the first), reason is contingencies involving legal issues about church and state in the U.S., and cultural hangups connected with this. For better or worse, it is likely that the Supreme Court would see a law grounded in the existence of God, even if the law included a preamble giving a very powerful rational argument for the existence of God, as violating the separation of church and state.
I have theistic friends whom I respect highly and who try very hard to avoid making use of the existence of God in their work in applied ethics. While I think such work is very important both intellectually and practically, I also think there is a danger of distortion in bioethics if one confines oneself to working in this way. When one does have to do non-theistic work in bioethics, one should think of it as a way of tying one hand behind one's back, because that's what the rules of the game call for, not because that's what is appropriate to the enterprise of truth-seeking. For when we are talking about appropriate treatment of the beginning and end of life, it is plausible that the question of the relation between life and God is highly relevant. Some people think that the way science can explain all kinds of facts without invoking God is an argument against the existence of God. That's a bad argument. But if ethics, especially the ethics that deals with the beginning and end of life, could do without God, that should be quite surprising to a theist.
In the above, I talked of mere theism. I have a strong suspicion that, at least in our fallen state, more than mere theism is relevant. John Paul II somewhere said that we can only understand man through Christ. If that's right, then non-Christian bioethics is doomed to incompleteness. And incompleteness in a philosophical enterprise runs the danger of leading to distortion, through onesidedness.