DUBLIN — In a century-old political system controlled by two seemingly indistinguishable center-right parties in Ireland, Jamie Clarke did what seemed sensible to him: He never voted in a general election.

Until Saturday.

“Fianna Fail and Fine Gael were the people that made the decisions, and someone like me could never change it — that’s the way it felt,” Mr. Clarke, a 33-year-old bartender, said on Monday, referring to the Irish political duopoly that has traded power since 1932. “I was so disaffected by how far they were from me.”

But in recent years, successive public votes in Ireland to legalize same-sex marriage and repeal an abortion ban have pulled many young and dissatisfied people into politics, giving voters a chance to shake up traditions that were once rigidly enforced by the Roman Catholic Church. Their next target was Ireland’s ossified political hierarchy.

On Saturday, voters cast off that relic, too, ending the two-party stasis in Irish politics with a breakout vote for Sinn Fein, a party long shunned by the mainstream for its ties to the Irish Republican Army, a paramilitary group that sought the reunification of Ireland. Despite what he called the party’s “shady history,” Mr. Clarke said, he voted for Sinn Fein because he felt it was the tonic that Irish politics needed.