From April 2006 through March of 2009, the Israeli government was led by the Kadima party with Labour holding the second largest number of seats in the Israeli Knesset. For the last nine months, the Likud party has been in power with Labour again, in the coalition. Now, we don't know of any rational journalist who would consider politicians in the Labour party "right-wing" and very few would characterize the Kadima party as such. Only politicians from Likud and other smaller parties like Yisrael Beiteinu are generally referred to this way in the media. So let's be clear: Israel has been led by a "right-wing" party for just 9 of the last 44 months. Moreover, leftist politicians, journalists, and powerful NGOs have remained a vocal minority in Israel during this time.
Now let's see how Reuters views things. With article archives going back to early 2007, entering the term "Israeli right-winger" on the Reuters website search engine produces 115 results. Entering "Israeli left-winger" yields 3.
We think those figures reveal much more about Reuters bias than they do about Israeli society.