JERUSALEM — The Israeli parliament approved the first part of Prime Minister Benjamin Netanyahu’s sweeping proposal to overhaul the judiciary on Monday, establishing a limit on the Supreme Court’s power to strike down government action and delivering far-right lawmakers a key victory in their bid to remold the country. The proposal passed despite hundreds of thousands of protesters turning out to oppose the measure, which critics said would erode one of the few checks on government power in Israel, a country without a written constitution. Supporters, led by Netanyahu, defended the changes are a necessary correction to judicial overreach. Both sides claim to be defending democracy.