Israel can Jewish and democratic if it agrees to a two-state solution with Palestine. This is something that Israel is vehemently opposed to. Without a two-state solution, Israel must annex the Palestinian Territories instead. By annexing the Palestinian territories, Israel could remain democratic, but split roughly evenly between Jews and Arabs, and therefore no longer remain Jewish; or Israel annexes the territories, suppresses the rights of Arabs, and ceases to be democratic.
A 2014-2015 survey by shows that Israeli Arabs generally do not think Israel can be a Jewish state and a democracy at the same time. This view is expressed by majorities of Muslims (63%), Christians (72%) and Druze (58%). Overwhelmingly, all three of these groups say that if there is a conflict between Jewish law and democracy, democracy should take precedence.