She was selected as the Fine Gael candidate in the November 2019 Wexford by-election, which was called after the election of Mick Wallace to the European Parliament. During the by-election campaign, Murphy made remarks supporting Noel Grealish's attempts to block a Direct Provision centre being created in Oughterard, County Galway, and suggested that immigrants coming to Ireland were being "infiltrated by ISIS" and would need to be "deprogrammed". She claimed that immigrants as young as "three or four years old" were a danger because of ISIS brainwashing and that ISIS is a “big part” of the migrant population in Ireland. These remarks were criticised by the Irish Refugee Council and by members of opposition parties in the Dáil. Murphy subsequently apologised for her remarks and issued a statement, stating "This was a very poor choice of words and I am very sorry to anyone who was offended by them. People coming here fleeing persecution deserve to be treated with compassion and respect. They need to be given opportunities to forge a new start for themselves and their families. That is why we have direct provision: to provide board and lodging to people seeking asylum". However, following the apology, Murphy released a campaign video on YouTube in which she claimed that "the victim of “character assassination in the media." This prompted the leader of Fine Gael and Taoiseach Leo Varadkar to comment directly on Murphy, stating the video was "bizarre" and "not party-approved". Several other top-ranking members of Fine Gael were also disturbed by her campaign, including TanaisteSimon Coveney, who stated that Murphy's comments were wrong, and her choice of language about migrants was not acceptable. On election day, Murphy received 9,543 first preference votes and was eliminated on the fourth count. Despite the defeat, Murphy insisted on election day that she would be Fine Gael's candidate in the 2020 General Election.
Removal from Fine Gael ticket
In December of 2019, Fine Gael de-selected Murphy as a candidate for 2020 general election as a result of her behaviour during the November by-election. When asked again about Murphy after the by-election, Leo Varadkar stated "quite frankly I'm glad she didn't get elected" and remarked; "What was done subsequently in terms of the video she did which sort of tried to imply the whole thing was a media character assassination attempt on her – I had a big problem with that because maybe it suggested to me that the apology and retraction wasn’t fully sincere." Furthermore, Varadkar declared that it had been a "mistake" by Fine Gael to select Murphy as a candidate, a mistake for which he took responsibility for. Following her de-selection, Murphy left Fine Gael.
