If there is a new world order or an Illuminati why do people think the members are only Republicans?

First I am not into grand conspiracies. In fact I find most of them just plain silly. However, everytime I see mention of these groups it seems they are almost always equated with Republicans. If there is a New World Order or an Illuminati isn't it much more likely that these groups would non specific in party affiliations and corrupt all politicians equally in order to achieve their goals.