Naszályi joined Politics Can Be Different (LMP) in early 2010. Her name appeared in the party's Budapest Regional List, but did not secure a mandate during the 2010 parliamentary election. She was elected into the local representative body of Budavár (1st district) during the 2010 local elections.[2] She also functioned as professional coordinator for the caucus of LMP in the General Assembly of Budapest. When the party's “Dialogue for Hungary” platform decided to split from LMP in February 2013, Naszályi was among the founding members of the new party, Dialogue for Hungary (PM). She retained her position in the local representative body of Budavár.[3] She was re-elected as representative during the 2014 local elections. She worked as an environment councilor within the local government for the next five years.[4] She was a member of the presidency of her party from 2016 to 2018.[5]
Initially, she was a candidate of the MSZP–PM electoral alliance for the position of MP for Budapest Constituency I during the 2018 parliamentary election, but, alongside other opposition politicians, withdrew her candidacy in favor of LMP politician Antal Csárdi.[6] She became a member of the General Assembly of Budapest in June 2018, replacing Sándor Székely, who was elected Member of Parliament two months before.[7] In accordance with their agreement on 6 April 2019, Naszályi was the joint candidate of opposition parties MSZP, PM, DK and Momentum for the position of mayor of Budavár during the 2019 Hungarian local elections; she defeated incumbent mayor Gábor Tamás Nagy (Fidesz), who administered the district since 1998.