Nazi refers to a very specific political movement (a party in fact) in history that promoted horrible ideas and perpetrated horrible acts. Aryan is a now largely unused term for an old way of understanding race that has been terribly stigmatized by its association with movements like the Nazis.
Jews, for anyone with a sensible understanding of history, have always been minorities, and have almost been discriminated against, often being the scape goats for social problems. They have frequently suffered consequences for this. We know that it is unreasonable to believe Jews are dominating everyone and gaming our system, etc... To think so would be crazy. And again, history has validated that, and expressing beliefs in unjust Jewish rule has been associated with delusional racist movements.
With those contexts on those words, there isn't a way to talk about Nazis or Aryan people in a positive or defensive let that does not sound terrible, and there is no way to talk about Jews exploiting people that doesn't sound crazy. So all one has to do to make any person, and their rhetoric, sound bad is replace whoever they are defending with Nazi/Aryan and whoever they defending against with Jew. It's universal. This in no way demonstrates that there was something wrong with the original, undoctored sentence.
I can do this with other words. I can do this by simply swapping the same two words within a sentence, because there in fact history has been different for different people. Look at these two sentences:
"For hundreds of years white people systematically enslaved black people"
"For hundreds of years black people systematically enslaved white people"
The first sentence is a statement of accepted history. The second sentence is the rambling of a madman. Leaving the structure of statements the same doesn't mean they are somehow equal. The insanity of the second sentence does not diminish the credibility of the first one at all.
But that actually gives this site too much credit. They aren't even generally trying to make something look bad, they are specifically trying to say feminist rhetoric sounds like Nazi rhetoric, and they do this by injecting words like Nazi into it! Well no shit it sounds like Nazi rhetoric now! It doesn't show "similarities between feminism and Nazism" (which is actually exactly what the site says it is attempting to do), it shows that any sentence sounds a lot more like Nazism if you make it involve promoting Nazis and hating Jews.