I find a significant lack of subtlety in this debate thus far. Current misconceptions of Ethical Nihilism has labeled it a denial of morality, but this is inherently untrue. It is a denial of the objectivity of morality. Thus, it presumes that we cannot determine absolutely and empirically that which is good and bad, rather we construct these values individually. Thus nihilism is not a contradiction, FBE, nor does it value apathy, MMEDM.
It means not caring about morals, and ignoring the relevance of all morals. It is the only way of not contradicting yourself. Objective morality is claiming morals but basing them solely on your life experiences and using a code that (undoubtedly) works for you on everyone else. How is that reasonable?
At least ethical nihilists aren't hypocrites. They just don't care.
Since to reject all religious morals you could not then be ethical. There are many ethics in religion worth following. If you were to rebuke them all you would be generally worse off.
Also its worth noting that this question cannot even be answered without being objective and subscribing to Objective Morality.
Moral nihilism (also known as ethical nihilism) is the meta-ethical view that nothing is intrinsically moral or immoral. For example, a moral nihilist would say that killing someone, for whatever reason, is neither inherently right nor inherently wrong. Moral nihilists consider morality to be constructed, a complex set of rules and recommendations that may give a psychological, social, or economical advantage to its adherents, but is otherwise without universal or even relative truth in any sense.
Moral nihilism is distinct from moral relativism, which does allow for actions to be right or wrong relative to a particular culture or individual, and moral universalism, which holds actions to be right or wrong in the same way for everyone everywhere. Insofar as only true statements can be known, moral nihilism implies moral skepticism.
Ethical Nihilism means not caring about the morals. This lack of morality creates issues because it gives people the option to commit acts against another person (murder, bodily harm) without the fear of morals and only the fear of the law. Whereas with objective morality, there are multiple factors that will affect a persons actions (morals), Ethical Nihilism removes that factor.