SYDNEY—Reserve Bank of Australia Gov. Philip Lowe looks likely to be unceremoniously removed from his job next month amid a new and worrying era of political pressure being exerted on the setting of interest rates, and growing doubts about the cherished independence of the central bank in the future. Treasurer Jim Chalmers said this week he will appoint the next governor in July, with the announcement coming just ahead of a list of potential candidates for the RBA’s top job leaked to national newspapers. Those...