I learned a number of things from my dad when I was growing up. One of the interesting things I learned from him was that normal people shave in the morning. Not that he did nor anyone else I ever saw shave, but that's besides the point.
The more relevant thing I learned from my dad is that it's important to be in the middle. Being in the middle means that you are balanced. Being on one side of the spectrum, for example a right winger or a leftwinger means that you are a bit radical. Nobody wants to be radical so they define the spectrum around themselves. I would like to say that I am the center, Likud is left, Kadima is very left, Labor is a bunch of nutcases and meretz is like martians they are so far out there. I would say marzel is slightly right wing and then there are other groups which are far right wing.
The slogan of the "right wing" should not have been "Moving rightwards", and their party should not have been called "the new Right". The message should have been, "come back to your roots" or "Don't be radical, vote for us", "All normal people vote this way", "Education is our middle name", "The pro children party".
I don't see religious issues as being right wing while left wingers can't follow mitzvot. In my mind, religion is the middle of the road. Anybody can do it. I also see settlements as a normal middle of the road part of Israeli society. It is not radical, it is not right, it is normal. One huge problem with the gazan refugees is that they define themselves as so far right that most of the population doesn't see them as having any connection to normal mainstream people. If they marketed themselves as normal mainstream, they would get a lot more sympathy and other people might identify with their plight. But really, who in Tel Aviv really cares about a bunch of far right wingers.