A Moderate is someone who feels that there shouldn't be moral absolutes to every question, and there are usually some truths in both the conservative and liberal viewpoint. Moderates tend to favor evolutionary political change rather than revolutionary change, perhaps because you never know what you're getting into when you abandon, or reform, a system that seems to work pretty well and try to make a new one from scratch. It’s hard to argue that gradual, careful change is wrong, so what do quite far to the right Conservatives do?
Rush Limbaugh and his ilk have labelled moderates as "worse than Liberals," the ultimate insult when used by stupid conservative hate-mongering racists. Andrew Schlafly contends that a moderate is just a liberal pretending to be "reasonable." He may have a point, because in this era of reactionary conservatives who are so far right they walk and talk like Fascists, moderates may actually vote for a liberal.
Are there any Moderate Republicans left?
Good question? While there have been no actual sightings of moderate Republicans at the Federal level since Nelson Rockefeller, There have been rumors of sightings.. These may be, in fact, traditional conservatives masquerading as moderates to find success in purple districts,. They may be moderate neoliberals pretending to be moderates, and if that's the case, they may have some claim to being moderate in a post-CU v SEC America sort of way. At the least, Moderate Republicans are an endangered political species, at worst they're extinct and were reluctant to admit it.
Moderate or Centrist?
A moderate, at least a traditional moderate back in the day, would be a moderate within the tradition of American liberalism. While, a centrist would have political beliefs near the center of the beliefs of the electorate, or perhaps beliefs which might overlap wings of both Parties. The Center of American Politics, whether it's the center of the electorate or between the Parties has been shifting to the right for decades, while moderate beliefs really haven't shifted. Hence the extinction of Moderate Republicans.