My understanding of the situation is more that the right has had many laws shot down consistently by the left leaning Israeli high court (equivalent to the supreme court in the US, except they choose their own judges, not the elected government). Recently, the right has come into a much stronger coalition (after numerous rounds of election over the past four years) and is now using the fact that they are unified enough to finally remove some (most?) of the power the court holds over the Knesset (parliament).
Concerns in Israel are that by defanging the Judiciary, the country will inevitably be at the mercy of the narrow majority. These concerns have economic and security as well as political basis, according to those who oppose the plan.