Legitimists
Affected by sinistrisme, few conservatives explicitly called themselves right-wing during the Third Republic as it became a term associated with the counter-revolution and anti-republican feelings and by the 1900s was reserved for reactionary groups. Those Legitimists who had rallied to the Republic in 1893, after Chambord's death ten years before still called themselves "Droite constitutionnelle" or "républicaine" (Constitutional or Republican Right). However, they changed their name in 1899 and entered the 1902 elections under the name "Action libérale" (Liberal Action). By 1910, the only group which openly claimed descent from the right-wing gathered only nostalgic royalists and from 1924 on the term right-wing practically vanished from the parliamentary right's glossary.
Christian right
The notion that conservative Christians want to reinstitute slavery and rule by genocide is not just crazy, it's downright dangerous. The most disturbing part of the "Harper's" cover story (the one by Chris Hedges) was the attempt to link Christian conservatives with Hitler and fascism. Once we acknowledge the similarity between conservative Christians and fascists, Hedges appears to suggest, we can confront Christian evil by setting aside 'the old polite rules of democracy.' So wild conspiracy theories and visions of genocide are really excuses for the Left to disregard the rules of democracy and defeat conservative Christians – by any means necessary.