It depends on what you mean by religious right. Neoconservatives have tended to be Jewish or Catholic, pro-immigrant and pro-civil rights, and so have traditionally been less than comfortable with Protestant fundamentalists. Major religious Catholic neoconservatives: Richard John Neuhaus (former editor of First Things- RIP), Michael Novak, George Weigel, Bill Bennett. Chuck Colson was one of the major figures bridging the gap between these Catholic neoconservatives and the Evangelical community.
Weren't many neoconservative originally Democrats, like Henry M. Jackson, but then they split with the party in the 70's when its dovish isolationist wing (George McGovern, Jimmy Carter) took over.
That's the "official" definition. In terms of the media it soon came to mean any conservative who supported the Iraq War pretty much. Or more specifically the Bush Administration.
