Since my answer is a bit nitpicky, I doubt that you'll be satisfied, and additionally I am not deeply knowledgeable about the current situation, howevr:
First, please note that fascism is not nazism.
Fascism: (from Wikipedia) Most scholars agree that a "fascist regime" is foremost an authoritarian form of government, although not all authoritarian regimes are fascist. Authoritarianism is thus a defining characteristic, but most scholars will say that more distinguishing traits are needed to make an authoritarian regime fascist.
For me the additional factor is that corporations and the government work together in a tight connection.
Given this, I would say that both Israel and the US are fascist governments. Both are a bit weak on the authoritarian aspect, but the US, at least, has been becoming increasingly authoritarian over the past few decades. I'm not sure about Israel. I have a feeling that Israel might be tending more towards a theocracy, but I have no direct knowledge.
OTOH, loosely used (as I suspect the grandparent was using it) fascism is a powerful group that uses its power to oppress those opposed to it. That clearly fits most existing governments, but people usually refuse to see that the definition is to broad to be of any use.
Thirdly, the fact that your family was victimized by some group 50 years ago doesn't prevent some group you currently support from practising the same tactics. I'm sorry if you find that comment distasteful, but it's also accurate.
As for the "anti-semetic" part, most of the Israelis are not Semetic. Many of them are ethnic Russians. There's a tangled history behind that, but most of the Semetic Jews are Shephardic. (Not all, but the Diaspora was a long time ago, and over the centuries there was a lot of interbreeding, joining by conversion, etc. to the extend that the non-Shephardic jews are only very slightly Semites.) So to be anti-semetic in this conflict you would be against the Palenestinians (who also aren't all that Semetic, but are more so than most of the Jews).