While still a university student, Hagiuda had become an aide to the Hachiōji city councilman Ryuichi Kurosu. In 1991, at the age of 27, Hagiuda himself was elected the Hachiōji City Council, becoming the youngest candidate ever elected to the council. Kurosu was elected to the Tokyo Metropolitan Assembly in 1993, but resigned in 2000 to run for Mayor of Hachiōji. Hagiuda was elected to his vacated seat in the Metropolitan Assembly. He then ran in the 2005 general election for the Liberal Democratic Party and was elected to the House of Representatives for the first time.
Following the assassination of Shinzo Abe, ties between Diet members and Unification Church came under scrutiny. Hagiuda was one of those alleged to have close ties to the group. An anonymous source claimed in a tabloid that Hagiuda had made regular visits to the Church in Hachioji during his time out of office from 2009 to 2012 and was "like one of the family." Hagiuda disputed these statements but admitted he had made speeches at affiliated organisations.[4]
When Kishida reshuffled the cabinet and party leadership in August 2022, Hagiuda was appointed Chairman of the Policy Research Council for the LDP.[5]
In December 2023, he resigned as Chairman of the Policy Research Council amid a financial scandal involving the Liberal Democratic Party.
Hagiuda is married, and has one daughter and one son. His hobbies include sports such as baseball, rugby, and golf. He also enjoys watching movies, holding movie-viewing events annually in conjunction with his personal support group, or koenkai. His personal website also lists "trying new restaurants" as a hobby, calling him a "self-proclaimed gourmet", and also mentions his frequent enjoyment of after-meal ramen.