They were both neoliberals who pushed deregulation. And both were union-busters. Carter was the beginning of that trend, in fact, putting an end to FDR's legacy. Reagan just did it more palatably, with a smile and a joke.
Despite being a union member and president of the SAG, Reagan is well known for firing the air traffic controllers. In California, he was against the UFW's grape boycott. As governor, he vetoed the legislation which would have given the farm workers the right to organize.
Reagan was unquestionably anti-labor despite perversely being inducted into the Labor Hall of Fame by Trump's Labor Secretary.