SYDNEY—A battle for control over Australia’s ruling coalition, fueled by policy disputes and personal vendettas, ended with the prime minister’s ouster but failed to close the rift that threatens the Liberal Party, the country’s dominant conservative force.
Scott Morrison, a Christian who backed greater rights for religious groups and once oversaw the offshore detention of asylum seekers, won a party vote on Friday and will lead the government to an election due next year. But his thin margin of victory at 45-40 over a more...