You are right that anti-Semitism has existed for thousands of years and will continue to exist after the State of Israel is disbanded. "It is halacha that Esav hates Jacob," our Sages say.

What we mean on the website is as follows. Anti-Semitism always exists in a latent form, but there have been times in history when it manifested itself in severe actions, and other times when it was kept at bay and Jews lives relatively peacefully. We believe that G-d watches over us in exile and does not allow us to be persecuted: "And even so, when they are in the land of their enemies, I did not reject them nor despise them&" (Leviticus 26:44). When we are persecuted, G-d has a reason for it. It's to keep us in line, to put a stop to assimilation, to show us that we shouldn't feel too much at home in exile. "And what you imagine will not come to be: you say, let us be like the nations, like the families of the earth, worshipping wood and stone. As I live, said Hashem G-d, I swear that with a strong hand and an outstretched arm and poured out wrath I will reign over you." (Ezekiel 20:32-33)

Nowadays there is completely new phenomenon: Jews are waging wars against gentiles, arousing their anger, which leads to the death of Jews. This is not the old persecution of the past two thousand years. Then it was not our fault we did nothing to the Germans or the Spanish or the French. Then it was G-d's doing, to teach us a lesson. But now it certainly is our fault, because we really are doing something to anger the gentiles and provoke them to attack us.

So when the State of Israel is disbanded, the Jews worldwide will be able to live in peace meaning that this danger we have brought upon ourselves will come to an end. Jews will go back to living in exile just as they did before at peace, unless G-d decides to bring persecution on us for our own edification.

As an analogy, imagine that someone said, "If only America and the USSR would stop antagonizing one another, there would be peace." And you would say to him, "What do mean there would be peace? Wouldn't there still be tornadoes and earthquakes and hurricanes? Do you call that peace?" The answer is, he meant peace from the artifical conflict created by the policies of the two nations. Of course there would still be acts of G-d, but that is not what he meant.