JERUSALEM — Sheldon G. Adelson is perhaps best known as a conservative casino mogul who spent tens of millions of dollars last year trying to defeat President Obama. But he is a larger-than-life lightning rod in Israel, too. He owns the largest-circulation newspaper here, a right-leaning tabloid which he calls “fair and balanced” but which some competitors denounce as speeding the decline of good journalism. He has sprinkled $200 million across the state’s hospitals, museums and universities. He is married to an Israeli, and close to Prime Minister Benjamin Netanyahu.