In its most basic definition, Punk music is a manifestation of the rebellious, anti-authority punk subculture that peaked in the second half of the 1970s, primarily in the US and the UK.Not just a music genre, but punk is more of an attitude, a philosophy, and a whole way of being.
Sure it doesn't sound like punk music, but they sure as hell ripped a massive middle finger at authority.
If you've heard their work, and understood who wrote it, you would know that Matty Healy is not a white supremacist. He's just a fucking idiot with a shit sense of humor. Kinda tired of people framing people as extremists when they made a few problematic remarks on a couple podcasts at worst.