Once upon a time there were anti-semites who wanted to promote their ideas in public and get away with it, but open anti-semitism was frowned on.
They needed some way to deny being anti-semites, while verbally attacking Jews.
One option they might consider is to say, "We don't hate Jews, we just hate Israel." This would let them say all the nasty stuff they want about the Jewish state, and the Jews there, while pretending not to be anti-semites.
This would get them a larger number of TV appearances, newspaper articles, etc, than if they introduced themselves as anti-semites.
No organization or cooperation or central planning is needed for this to become commonplace. Once a couple people try it out, and get publicity, then others will see its effectiveness and can copy the technique.
Today this technique is a daily occurrence. It's used to repeat traditional anti-semitic propaganda with only slight changes.
For example, "Jews murder Gentiles for pleasure or ritual" becomes "Israelis murder Palestinians for no reason" (except that, apparently, they wanted to).
"Jews kill babies" becomes "Israel is a child-killer state."
"Jews cheat at business and steal" becomes "Israeli settlers, especially right-wing orthodox Jews, steal land and water."
"Jews (via conspiracy) orchestrate major world events" becomes "the influential Jewish lobby is behind X"
Blaming Jewish victims for provoking their murderers is a staple of traditional anti-semitism, and of the "anti-Israel" rhetoric today, which finds ways to blame the Jews that Hamas kills.
So when someone says "I'm not anti-semitic, I'm just saying there are legitimate criticisms of Israel," and then says exactly the same things he would say if he was anti-semitic, he is either anti-semitic, willfully closing his eyes to anti-semitism, or extremely naive or ignorant.