BERLIN—German lawmakers have overwhelmingly backed a bill that requires staff at hospitals and nursing homes to get vaccinated against COVID-19. Of the 689 votes cast in the lower house on the measure, 571 were in favor and 80 were against. Abstentions were recorded for 38 lawmakers. The bill, which is being fast-tracked, still needs to be approved by the upper house, which is likely to happen later Friday. Health Minister Karl Lauterbach told parliament it was unconscionable that some who work with particularly vulnerable people are still not vaccinated. “This vaccine mandate is necessary because it’s completely unacceptable that, after two years of pandemic, people who have entrusted their care to us are dying unnecessarily in institutions because unvaccinated people work there,” he said. “We cannot accept this.” The bill is the first of two vaccine mandates that were being considered in Germany. A second, more contentious bill that would …