When Ready for Hillary, a pro-Hillary Rodham Clinton “super PAC,” wanted to take out a million-dollar loan five months before it planned to go out of business, it turned to a bank that was founded to guard the savings of New York City garment workers.When the Democracy Alliance, an influential club of liberal donors, sought to recruit members in advance of the 2016 elections, the bank’s president helped to make introductions.And when workers-rights groups wanted to embarrass Walmart and the Gap for unsafe working conditions at factories supplying their stores, Amalgamated Bank, which manages $40 billion in pension fund assets,...