A member of the Minnesota Democratic-Farmer-Labor Party (DFL), Finke represents District 66A in the Twin Cities metropolitan area, which includes the cities of Falcon Heights, Lauderdale, Roseville and Saint Paul, and parts of Ramsey County in Minnesota.

[5] In late 2022, she was publicly critical of Republican gubernatorial candidate Scott Jensen for spreading the transphobic litter boxes in schools hoax.

[1] Finke supported legislation to ban the use of the discredited practice of conversion therapy in the state for minors and vulnerable adults.

[11] Finke sponsored legislation to remove language associating sexual orientation with pedophilia in state law and adding gender identity as a protected class in Minnesota's human rights statute.

[12][7] She also wrote a bill that would repeal a law that criminalized knowingly exposing someone to HIV, calling them "old, outdated homophobic statutes".

[10] She has also spoken about the need to remove barriers to access to healthcare, including by increasing health insurance coverage.

[17] Finke sponsored an executive order protecting access to gender-affirming care for Minnesotans that Governor Tim Walz signed on March 8, 2023.