I don’t know what planet you live on but no foreigner can swing an Israeli election. Netanyahu alienated some of his top allies in his party with his long-time rival David Levy swinging over to Labor. He entered that election with a house divided. Then Barack promised 30,000 jobs which brought him a chunk of the Russian vote that Labor never gets.
Barack never created one job and Levy quit on the eve of the Camp David talks saying in effect that Barack was nuts. That ended Levy’s previously illustrious political career.
I don’t recall any foreigner managing the protests. This country operates in Hebrew and if you speak with a heavy accent no one is going to pay much attention to you.
I don’t know what planet you live on but Goldstone Report did matter. NGO support from the likes of NIF does matter. Soros does matter. We ignored him and the Shadow Party in the US and got Obummer (see David Horowitz’s prescient book).
As to influencing Israeli elections, I guess you never heard of James Carville, Clinton’s man and sometime advisot to Ehud Barak. Do you think the US had advisors to Sarkozy and Cameron’s opponents?