My mother-in-law has just arrived from Israel for her summer holiday. First she coos over her grandchild. Then we sit on the floor and unwrap the beautiful pots and cups that she has made for us. We chat about how things are in Tel Aviv – the people, the weather, new restaurants. Soon enough we turn to politics. Here the mood changes. Great place, Israel. Terrible politics.

Prime Minister Benjamin Netanyahu staged a rally of his supporters last week. In the face of mounting accusations of corruption, he hit back at the media and the liberal elite who he says want to unseat him. “Fake news,” he called it. Such are the similarities between Netanyahu and Donald Trump, it is hard to know who is copying whom. Netanyahu deliberately plays up the connection. Which is why events in Charlottesville, and Trump’s half-hearted condemnations of US fascism, have given Israel’s PM a political headache. Condemn Trump and he risks alienating his political soulmate. Not condemn Trump and he looks like being soft on neo-nazism.

Most Israeli politicians got it right. Reacting to Trump’s “there are two sides to every story” line, Yair Lapid insisted: “There are no two sides. When neo-Nazis march in Charlottesville with antisemitic slogans against Jews and for white supremacy, the denouncement is unequivocal.” But Netanyahu took three days to come up with a condemnation of neo-nazism, slipped out in an English-language tweet. Should it really have been so difficult for an Israeli PM to condemn nazism?

A problem for the Israeli right is that there are quite a few, especially on the outer fringes of rightwing politics in the US, who don’t much care for Jews, but purport to admire and support Israel because of its commitment to maintaining a particular racial majority within its borders.

Speaking on Israel’s Channel 2 News on Wednesday, the alt-right’s Richard Spencer, one of the leaders of the Charlottesville rally, gave an astonishing example of this “antisemites for Israel” philosophy. “Jews are vastly over-represented in what you would call ‘the establishment’ and white people are being dispossessed from this country,” he said of the US. Yet he continued: “An Israeli citizen, someone who has a sense of nationhood and peoplehood, and the history and experience of the Jewish people, you should respect someone like me who has analogue feelings about whites. You could say I am a white Zionist – in the sense that I care about my people, I want us to have a secure homeland for us and ourselves. Just like you want a secure homeland in Israel.”

This is staggering stuff. Richard Spencer is the man who chanted “Heil Trump” during a Washington rally. His followers responded with the Nazi salute. Praise from a man mired in the worst sort of antisemitism should prompt soul-searching on the right of Israel’s political establishment. These are not admirers that they should want.

More shocking, some concede that Spencer and his like have reason to find common cause with some of Israel’s outer political fringes. As the former PM Ehud Barak said of Charlottesville: “You can’t say you don’t see things here that bear a certain similarity – when you look at the Lehava demonstrations or La Familia activity, or the ranting against journalists covering Netanyahu investigations.”

Lehava is an acronym of the Hebrew for “Prevention of Assimilation in the Holy Land”. It is especially against mixed marriages (like mine) between Israeli Jews and non-Jews. And it also wants to rid Israel of Christianity. La Familia are fans of the Beitar Jerusalem football team. A few months ago I went to see them playing an Israeli Arab team from Galilee, Bnei Sakhnin – though the Sakhnin fans were not allowed into the ground. My remedial Hebrew was not enough to make out what they were singing to the rows of empty seats opposite. “We are going to burn your village down,” was how my friend translated it.

Barak is right, the parallels with Charlottesville are sometimes difficult to avoid. And the problem everywhere with these outer fringes is that they are getting less and less outer. Frightening, isn’t it?