First off, we will consider amoral and immoral to be close synonyms. They aren't necessarily, since amorality under certain circumstances denies the existence of objective morality. But the author of the quote doesn't study moral skepticism, and clearly considers them to be close synonyms.
In remaining neutral in the face of a great evil, are you not essentially aiding the evil by your silence? Does a moral stance not necessarily include standing against the immoral?
There is a problem here, I think. Morality can be defined several ways, two of which are necessarily contradictory and cannot exist at the same time.
There is the DESCRIPTIVE definition. That is, morality is the set of codes which are bound in your society. It is subjective. What is considered immoral to you is not necessarily considered immoral for a person from Botswana and vise-versa.
There is also the NORMATIVE definition. That is, that there is an objective moral code. Most modern ethicists see that there are certain universal ideas on morality which exist in nearly all cultures and these can be said to be objective. Alan Donagan bases his argument in "The Theory of Morality" on this idea.
But an easy difference between these two is the former says "I believe this is immoral" or "most believe this is immoral" and the latter says "this is immoral". There is a mountain of difference between the two.
Let's use two cases for examples, both historical.
1. The Holocaust.
2. Female Suffrage.
Let's start with the first.
Let us assume that you are a person of power during WWII. And you have knowledge of the Holocaust--whether or not the powers that be at the time knew or could have done anything is irrelevant, let's assume that you know.
Now, in this situation, a DESCRIPTIVE and NORMATIVE definition equate roughly the same. There is not an ethical system or moral code which permits genocide--even those who commit it are aware that it is immoral, but the deem the supposed necessity as justification for abusing their own moral code. Neutrals are not hindering German genocide, so they are essentially aiding it by making the German military's job that much easier. And indeed, you could very easily by indirectly aiding--because the Allies may need to guard their shipping lanes through your waters even more closely because the Germans know that they can operate with impunity and therefore take losses elsewhere.
And is it not immoral to aid a great evil?
By this, is is immoral to be neutral.
Second. Female suffrage.
Now, in the Descriptive sense... Person A considers female suffrage to be immoral. But this is just their point of view. But now let's consider that Person A also decides to stay neutral on the issue. For whatever reason.
Now, by not standing against the evil that he thinks female suffrage is, he is helping the cause of female suffrage. By not standing up and voting against it, he is allowing the suffragettes to require one less vote in their favor.
In the normative sense, I don't think female suffrage can be said to be against any sort of objective moral code. It is not onerous, it cannot be considered unjust to allow someone the option of participating in their own government, it does not unjustly limit, no on is harmed, etc...
Therefore, to remain neutral is merely remaining neutral. It really is neither immoral nor moral.
"There is a fine line between neutral and amoral. In fact, there may be no line there at all."
Accepting that amoral and immoral in this case are close-synonyms, we can therefore say that...
Yes, there may be no line there at all.
In cases of clear moral violations, you are certainly obliged to fight the immoral and neutrality is tantamount to aid.
In cases of blurry moral violations, either you see something as immoral--and therefore the previous clause comes into play--or there isn't a moral issue and therefore no line to begin with.