Useful idiot

The various modes of worship which prevailed in the Roman world were all considered by the people as equally true; by the philosopher as equally false; and by the magistrate as equally useful. A useful idiot is someone who supports one side of an ideological debate, but who is manipulated and held in contempt by the leaders of their faction or is unaware of the ultimate plan driving the ideology they subscribe to. The term originated in early 1950s America in reference to members of the Socialist Party, allegedly promoted by the malevolent KGB to weaken America as a nation. The closely related term fellow traveler (Russian: спутник, sputnik) refers to one who sympathizes with and is willing to support the publicly stated goals of the Party while not being a dues-paying, card-carrying member. The phrase's origin has often been attributed to Vladimir Lenin, but there is no evidence that Lenin ever said or wrote it.

Co-optation
The term co-opted is often used when this phenomenon occurs on a sufficiently large scale that a group, movement, or cause has been appropriated and subverted to a hostile and destructive purpose.

This may be a conscious and organized effort in the case of agents-provocateurs; indeed, this would then be more or less precisely the aim. Alternatively, it may simply be the extreme natural consequence of Poe's law in operation when trolls and edgelords (for lack of more precise and neutral terminology) enter the community of interest in sufficient numbers to distort its aims, methods, and publicly-visible message.

The distinction, of course, is only one of conscious intent; the practical outcome for the community in question is essentially the same.

Citing specific examples is a contentious exercise, particularly in the second case.

Misuse
As a subjective label, the term is often abused. There are reasonable differences on matters of rhetoric and tactics in any ideological movement, but these differences can be unjustly smeared as idiocy with this label. Nor are all poor representatives of a position necessarily useful idiots: a useful idiot is a poor representative raised as a figurehead by a third party with malign intentions. VenomFangX might be a spectacular failure at Christian apologetics, but he's not a useful idiot because his popularity derives from other Christians, not atheists.

Alleged examples

 * S. E. Cupp — The atheist who hates atheists. She is frequently considered a useful idiot of the Religious Right, an atheist who talks in detail about how atheists are sexist, evil, silly, or unreasonable.
 * David Frum — An American conservative blogger, he is thought by many on the left to be "the reasonable one" and many on the right to be a useful idiot of liberals.
 * Kent Hovind — A creationist and evangelist with a diploma mill doctorate and a 10-year jail sentence, his tactics were scorned by more "respectable" creationist agencies like Answers in Genesis, who considered him well-meaning but a useful idiot for the villainous Darwinists.
 * The Tea Party — Many of the people who participate in "teabagging" protests have low incomes and might benefit from many policies supported by Democrats like Obamacare, and would mostly be hurt by Republican policies such as Paul Ryan's "Path to Prosperity," even though quite a few of them are opposed to cutting government programs such as Medicare and Social Security. (GOP strategists are aware of it.) The Republican establishment's catering to them in the name of votes eventually turned around. It bit them in the ass when the Tea Party movement by and large coalesced around Donald Trump's Presidential campaign in 2016, with his economic populism running counter to GOP orthodoxy regarding free trade and free markets.
 * Edward Snowden — After striking a blow against the abuse of civil liberties by the Bush and Obama administrations, Snowden allowed himself to get manipulated into a transparent public relations stunt by his ostensible protector, Vladimir Putin. To his credit, Snowden was fully aware of how that played out and was horrified by it. He took to the pages of The Guardian to make clear his rejection of Putin's "answers" and to explain his own intentions in asking the questions.
 * Henry A. Wallace — The former Vice President under Franklin D. Roosevelt ran on a third-party platform in 1948 that was staunchly left-wing and pro-Soviet. While it is widely agreed Wallace himself wasn't a communist, it's also broadly accepted that the party itself (the Progressive Party of 1948) had been infiltrated by genuine communists and fellow travelers. The Communist Party USA endorsed him in a "popular front" strategy rather than run their own candidate. As a result of his refusal to disavow them, the anti-communist Socialist Party ran their own candidate (the perennial rather than endorse Wallace. In his 1952 autobiography Where I Was Wrong, Wallace himself later admitted that he felt he had been duped by Josef Stalin and that his support for the Soviets stemmed from ignorance as to Stalin's true intentions and the nature of his rule.
 * Scottie Spence — The founder (and criminal) of Smoloko News, an anti-Semitic, International Jewish Conspiracy "news" service who sympathizes with Hitler and the Nazis treating them as if they were the good guys, utterly unaware of the less than noble things they did to Jews and pandering to the likes of Henry Makow, The Daily Stormer, and Real Jew News. He also serves as a useful idiot for Russian President Vladimir Putin. His female servant (or buddy) Alicia Frischmann also falls under the same useful idiocy for Nazism.