My guess is Propagandhi. The line "What it means to be a man, and what it means to refuse it" seems to refer to "Refusing to be a Man" from "Less Talk, More Rock". The lyrics also imply the band has been around for over 20 years, and Propagandhi formed in 1986.
Also, in the track-by-track interview, Rody says "I consider them an inspiration both musically and morally" and "I want to be a better person when I listen to their music", which makes sense based on the strong messages (political, humanitarian, animal rights etc.) Propagandhi get across in their music.