Average Israelis are afraid of the so-called "fanatical settlers" similar to how average Americans fear/hate the "religious right".
I think you are using too strict of a parallel between what happens in America with what happens in Israel, and you are equating apples with oranges here. These are two very different places with different populations. Not everything can be universalized. Most Israelis agree with the goals of settlers, even the most "fanatic" settlers. I would say probably most Israelis think the settlers (and especially the "fanatic" ones) are unrealistic or impractical, even though they sympathize with them. (Afterall, we HAVE to do things in such and such way, we HAVE to please America, bla bla bla etc - all the erroneous arguments I hear from Israelis on facebook and in Israel).
The American left and general public looks very differently at the right or religious right. They mostly do not agree with their goals and have completely different ones.
Look at how the government/media was able to bamboozle the public into hating the Charedim a couple months back because of the alleged incident that took place involving those unhalachically-dressed "Modern Orthodox" children,
Not on the point about the media - I'm just wondering -
Who was "unhalachically-dressed?" Review the video tapes, the children are dressed according to halacha (btw, the stringent dress code we adults adhere to is not even required by halacha for kids below a certain age. Nonetheless, these kids still are dressed in accordance with those laws that apply to adults!) It seems some people want to make up their own halacha.