Utilitarianism does have a moral principle: it is the principle of greatest good.
I'm not sure why you consider this a moral principle. The principle of the greatest good is not concerned with the rightness or wrongness of an action, only with whether it increases or decreases the sum total of happiness in the world.
That's much more a calculus of efficiency or convenience than it is of morality.
If morality is to mean anything, it means doing something because it is right even though it is more inconvenient or efficient for the individual or society.
Utilitarianism (or the principle of the greatest good) can provide input to moral decisions, but by itself it is not a moral principle.
If utilitarianism were to have a moral issue, it would be the demonstration that an increase in the total good is always right. As I understand it, utilitarianism fails to make that demonstration, but rather assumes it, making all the subsequent calculations on how to achieve that greater good morally unsupported.
Should say: “If morality is to mean anything, it means doing something because it is right even though it is less convenient or efficient for the individual or society.”
There are various moral or ethical theories only one of which can be right if morality is an objective quality, which I believe it is.
We can talk about all of the moral theories and say that X theory claims that an act Y is moral because of Z. The utilitarians (or those more commonly called consequentialists) believe that an act is moral if the positive consequences of that act outweigh the negative consequence. So we can claim that they have a moral theory and that theory is based on consequences. This is what I meant by my comment. They are not as directly concerned with "human character" as say virtue ethicists are, but they would be interested in human character indirectly if it can be shown that the development of good human character is a benefit that outweighs the negative consequences, i.e. people sacrificing their lives for others.
Now if it happens that consequentialism is wrong, which is what I personally believe for lots of what I claim to be very good reasons, then they could be engaging in acts which are without support and potentially immoral.
(BTW, the one good thing about consequentialists is that they do believe in objective moral standards. So at least they are not silly self-negating relativists.)
Those beliefs of Peter Singer that the essayist brings up may be incorrect, but they are not inconsistent, at least not based on the poor argument made by the essayist. Peter Singer is not an idiot. He is wrong and misguided in my opinion, but the error he has made is at the very beginning and not with any of the carefully drawn conclusions he makes from those initial, and incorrect, assumptions.