“Billy Bigelow hits Julie Jordan. Henry Higgins molds Eliza Doolittle. Fred tames Lilli. And Edward rescues Vivian. Amid a national reckoning with sexual harassment and misconduct, Broadway is mounting a cluster of musicals this season and next that, some theatergoers already contend, romanticize problematic relationships between women and men.” Michael Paulson looks at how the producers and directors of these shows are dealing with these problems.