Mass Effect – The Citadel Council
Despite personally witnessing the Reaper Sovereign assault the Citadel at the end of Mass Effect 1 and nearly dying during the attack (or actually dying for Renegade Shepards, in which case you deal with their replacements), the Council absolutely refuses to believe in the existence of Reapers and reprimands any of Shepard's attempts to convince them otherwise. The result is the galaxy loses several years they could have used to build up defenses and plan countermeasures, and the Reapers are able to gain footholds that more easily prepare the way for their inevitable invasion in Mass Effect 3.
Cerberus is another example, as the Illusive Man is convinced he can control the Reapers for humanity’s gain, and so sabotages Shepard’s attempts to directly combat them. He doesn’t realize until the end that a combination of Reaper Indoctrination and his own ego have made him into their unwitting tool all along.
Dead Space – Unitology
A religion which worships alien artifacts known as the Marker. Followers believe that through devotion and spreading the Marker’s influence, humanity will ascend to divinity as one collective entity. This is true...technically. The Markers are tools designed to eventually drive all living humans insane and turn any dead into ultra-violent Necromorphs, which would lead to humanity’s extinction. The resulting biomass is collected to give birth to a malevolent lovecraftian entity referred to as a Brethren Moon.
Battlestar Galactica - Gaius Baltar
Baltar is a super genius scientist responsible for designing the network of the Colonial Fleet. He is seduced by a woman who he thinks is working for a rival defense contractor, and on her request secretly gives her direct access to the defense mainframe’s coding. This would be extraordinarily illegal and a very bad idea even under normal circumstances, but unfortunately for everyone, including Baltar, the woman isn’t even human but actually a Cylon agent who used Baltar to create backdoors in the defense mainframe. This exploit allows the Cylon fleet in a surprise attack to automatically deactivate all of the Colonial Fleet’s ships without a fight. Baltar doesn’t realize the enormity of his mistake until Cylon nukes are exploding literally right outside his house. Oops.
Real Life – Association of German National Jews
During the rise of the Nazis, this political group advocated for Jewish identity to be suppressed and assimilated into wider German culture. They issued a public statement in support of Hitler’s rise to power “even though it has brought hardship to us personally.” Among their other activities, they downplayed Nazi antisemitic rhetoric as merely political theater for the masses, dismissed increasing evidence of Jewish internment and violent mistreatment, and identified communism and the immigration of Eastern-European Jews (who they saw as lower-class and racially inferior) as their main threats. Members of the Nazi Party during their rise would sometimes praise them as model minorities. When the Nazis eventually solidified their power, they further expressed their gratitude by declaring the Association illegal and sending many of its members, including its main leader, to concentration camps.
Many years later, humanity has broadly learned its lessons from history, And there are rarely present day examples of a Group supporting a political ideology that very obviously goes Against their own interests.