Rise of social (especially religious) conservatism, GOP losing a lot of strength in urban/suburban areas (Which NJ is basically 100% urban/suburban), Fast minority growth
As for 88 --> 92 specifically, George H W Bush performed amazingly in suburbs in general in 88. Part of this was many NJ suburbanites were concerned about rising crime rates, and Dukakis seemed useless and even dangerous for solving this issue to many people. Bill Clinton, meanwhile, seemed much better on this issue, and people were getting tired of republican presidents with the declining economy.
That pretty much hits the nail on the head. Especially the minority growth part.
