Europe during the Protestant Reformation saw some of these...
Europe during the Protestant Reformation saw some of these, most notably the so-called "Münster Rebellion" whose leader, John of Leiden, "claim[ed] to be the successor of David…[with] absolute power in the new 'Zion.' He justified his actions by the authority of visions from heaven….. He legalized polygamy, and himself took sixteen wives, one of whom he beheaded himself in the marketplace.
Converted by Christian missionaries, he came to see himself as Jesus' younger brother, ordained by God to overthrow the oppressive Manchu regime. He and his followers conquered Nanjing and ruled from there for about 11 years before being annihilated by government forces.
Other self-styled christs, such as Jim Jones (killed, along with his followers, in 1978 by drinking poison at their compound in Guyana, South America) and David Koresh (killed along with his followers by the American Bureau of Alcohol, Tobacco and Firearms in an assault in 1993 in Waco, Texas), might be seen as somewhat analogous to false mahdis but they never even came close to taking power.
Much more research and thought needs to go into explicating this clear difference on this point of political history between the world's two largest faiths, Christianity and Islam; but three historically- and theologically-grounded theories come to mind: Jesus specifically eschewed political power when he answered the question of Pontius Pilate, the Roman governor, "Are you the king of the Jews?" with "My kingdom is not of this world" (Gospel of John 18:33ff).
This has made it problematic for any of his followers to try to create the kingdom in the here and now-although some, as aforementioned, have tried. the careers of Jesus Christ and were rather different with respect to political power: the former never held it and the Christians were, for three centuries, a persecuted minority in the pagan Roman Empire, not gaining power until Constantine's time in the early 4th century CE.