Complex sentence: Studio mogul Goldwyn wanted Kaye's prominent nose fixed to look less Jewish, Kaye refused but did allow his red hair to be dyed blonde, apparently because it looked better in Technicolor.
Split into simpler sentences: Studio mogul Goldwyn wanted Kaye's prominent nose fixed to look less Jewish, Kaye refused. He did allow his red hair to be dyed blonde, apparently because it looked better in Technicolor.