Q:

What is the fascist argument for Marxism being a Jewish conspiracy?

How do fascists reason that communism is a Jewish conspiracy? 
To me general fascist / white nationalist rhetorical strategy seems like a complete refusal of approaching communism on its own terms. In my experience reading their rhetoric online, most white nationalists and fascists absolutely refuse to criticize their opponents by using the terms and ideas employed by their opponents. Instead they merely reverse psychologize counter arguments, while bastardizing concepts like genocide, ethnic cleansing, and Zionism. 

A:

The association of Jews with various left-wing forces can possibly be traced to the Great French Revolution.
At the time the rights of Jews in various European countries were severely restricted and assimilation was very difficult because of Christian anti-seminitism.
Thus the Jews welcomed very much the revolution that removed any civil restrictions on the Jews and was militantly anti-religious (even Christian priests for a period were replaced with "civil priests").
Thus the Jews became viewed as the enemies of the established order: the monarchy, the Christianity and the traditional values.
This was especially visible in Eastern Europe where the population was more religious and in Russian Empire where there were very harsh anti-Jewish laws intended to persuade them to convert to Christianity. 
Jews also were viewed as unpatriotic and foreign agents, which was partly true because Jews mostly were against nationalism, segregation, wars and did not experience very good feelings to the anti-semitic host state.
As such, most monarchists and conservatives in Eastern Europe and in Russia, such as Russian Black Hundreds became highly anti-semitic, with Jews on the opposite becoming pro-revolutionary.
As such, the conservative, right-wing monarchist forces started to link the Jews with any left-wing movements. This was not that complicated because Marx was a Jew, and many revolutionary leaders also were Jews. Particularly, they alleged that Jews wanted the revolution so to replace Christianity with Atheism, and then, probably, Judaism, because they hated Christ and Christians. 
In Italy there were no such processes, at least to the same degree as in Russia, so fascism as an ideology was not that anti-semitic.
But Hitler was more influenced by Russian far-rights, white emigrants and the Black Hundred, especially given that in Austria similar processes were taking place. 

A:

You've got to remember that prominent communists were Jews, Trotsky being the most obvious.  During the German Revolution in 1918 the rebel communist leadership was disproportionately Jewish.  Karl Marx was Jewish too.  
In much of Europe Jews had been excluded from most professions and forced to live in ghettos.  Gentiles simply didn't encounter Jews, and when they did their initial reaction was suspicion and prejudice.  Anti-Semites began to interpret what they saw as evidence of a conspiracy; between wealthy Jews in finance, Jews in the media, and communist Jews.  
The simple truth was these were some of the few professions and organisations Jews were able to access.  But that fact, and any ideological specifics, were irrelevant in face of this paranoia.  Plus fascism is generally anti-intellectual; so a reasoned argument is irrelevant when they feel something is true based on their anecdotal observation.  
EDIT [to clarify Trotsky, etc]:
It's important to remember that the traditional Jewish view of who is a Jew is based on the continuity of the maternal line.  Was your mother a Jew? And her mother? etc. Whether one practices Judaism or not is rarely considered qualifying. There are still lots of debates, legal and religious, in and outside of Israel regarding this very issue. 
Trotsky's atheism is irrelevant. Anti-Semites rarely consider renunciation of faith sufficient to prove non-Jewishness.  For example the Spanish Inquisition was paranoia about secret Jews. Sometimes even generations after their ancestors converted to Catholicism. This was complicated by the fact some Jews who converted did secretly practice their old faith, and passed this down to their children.  
Also keep in mind that anti-Semitism often insists that the Jews are a "race" of their own. In this case they viewed all Jews as a monolithic danger; a Jew is always a Jew. So what difference does it make that they are atheist, or go to church? They will always work to benefit their race. 
That was the idea anyway, and we still see it playing out in contemporary anti-Semitism, with suspicion that Jews are only loyal to Israel.  Perhaps that in itself is a projection of fascist values and attitudes; the belief that they must work to protect their own "race" against enemies, therefore they would naturally assume other races would do the same.  

A:

TL;DR: Marxism and Nazism are just two competing ideologies, so they thought of some dogmatic ideas to criticize each other. Their goal was to win the competition between the two ideologies, so virtually none argument was based on any solid, scientific research; instead, most (all?) of the arguments appeal to the senses, not to the minds.  

In order to completely answer this question, it may require a book to cover all aspects, so please excuse me for losing accuracy in favor of compact answer.
First off, Fascism and National Socialism are different things: Fascism is a regime (type of government), while National Socialism (Nazism) is an ideology. Between WWI and WWII they used to be tightly related, but they are not the same.
Note: Regardless "National Socialism" contains a word "Socialism", which suggests a counter-intuitive understanding, it has nothing to do about the type of the government:

Our adopted term 'Socialist' has nothing to do with Marxist Socialism. Marxism is anti-property; true Socialism is not. — Hitler, 1930 (ref. Carsten „The Rise of Fascism“, 1982)

The Kommunist counterparts are Socialism (a regime) and Marxism (an ideology). They also used to co-exist in the Russia and the countries it occupied.
As far as I understood your question, we are not talking about the social system, but about the ideologies.

Nazism is an ideology of racial supremacy. It included several aspects like "racial hierarchy" where Aryans supposed to be the "master race", while others are "lower" ones. The special attention was directed towards antisemitism as Jews were declared the "worst" race.
Marxism is an ideology of class supremacy. It included several aspects like "class hierarchy" where Proletariat supposed to be the "master class", while others are "lower" ones. The special attention was directed towards Bourgeoisie as they were declared the enemy who exploits the proletariat.
Being two competing ideologies, both Nazism and Marxism have elaborated some dogmatic ideas to confront each other. Here can be a huge list of arguments, but they are really unimportant since all of them are artificial, deliberately created in order to withstand each other.
Anyway, the ideology struggle had not in any way prevented the Soviet Russia and Nazi Germany to be loyal allies in the period of 1933-1941.
An important aspect is that the vast majority of Russian Intelligentsia of mid-1910's who led the October revolution were ethnic Jews. This may make someone think that Marxism is a kind of Jewish conspiracy. However, Marx's own views were arguably anti-Semitic:

What is the worldly religion of the Jew? Huckstering. What is his world god? Money. — Marx, „On the Jewish Question“, 1844; (ref. Francis Wheen — „Karl Marx: A Life“, 2001)

Yet another important aspect is that after defeat of Nazi Germany, the Soviet lawyers in Nuremberg trials have insisted to add Anticommunism in a list of Defining
Characteristics Of Fascism.

