Everyone needs an onramp to discovery. There are WAY worse things to be into than Green Day. But please, don't let me stop you from telling Hacker News how you're too punk for Green Day...
I never was a big fan of Dookie but their next album, Insomniac, is still an immensely enjoyable album to this day. Whether it's technically not 'punk' and is instead 'pop-punk' or just 'rock' makes no difference to me. The fact that their music isn't overtly anti-establishment doesn't affect the quality of the music.
In fact, and this may get me into trouble here, I like the Dead Kennedy's 'Plastic Surgery Disasters' just as much as I like Green Day's 'Insomniac'. Is one punk and one not? Who cares? I quite dislike the purity tests in some genres of music (like punk and metal). That's something I've always appreciated about pop music - it doesn't have to adhere to some nebulous framework to qualify for the genre, it simply has to be popular (e.g. Beatles were pop, Madonna was pop, and Arianna Grande is pop - very different styles of music)
The difference between "Lookout! Green Day" and "Warner Green Day" is one of DIY vs Payola. These days, it's much easier and potentially more profitable to go the DIY route, but back then, you needed a sugar daddy to "make it big" fast. Taking the easy route meant Green Day were shunned by their original fan base (somewhat justifiably so,) but they had more energy, raw talent, and Buzzcocks hooks than anything else on top 40 radio with the exception of Nirvana (which is why Warner was trolling for talent in the first place.)
It's hard to call any "punk" bands sellouts after Nevermind. Were Hüsker Dü sellouts? They signed to Warner in '85 (almost a decade before Green Day.)
The music business is harsh. If you're in a band and into it for the long haul, own your masters and go the DIY route. Your fans will find you and are more likely to pay directly when they do. If you're in a band and want to make it big fast, consider this often cited article from Steve "Mr. Gold Bracelet" Albini on cashflow:
https://www.negativland.com/news/?page_id=17
There's a reason you're seeing a lot of live music. Streaming doesn't pay the bills.
I listened to Offspring's album "Smash" a bunch in middle school, which made for an interesting revelation when I devoured Bad Religion's entire catalogue in high school.
Apparently The Monkees were also written up in Punk, are we calling them punk now?
I don't think Green Day counts as punk rock, because actual punk rock was about a lot more than the music... so Survival Research Labs, f'rinstance, was definitely punk in my book... and so were Nazi skinheads, although they sucked. But as you say, opinions vary.
If you've read the Monkees writeup in "Punk", it's a snide hit piece the thrust of which is "these guys represent everything we're not". Punks hated hippies, and fake Madison-Avenue canned hippies were considered about the lowest of the low.
Personally I'd rate the Monkees a bit better than that, once they started dropping acid... anybody who gave me Head surely can't be all bad!
Nazi skinheads are alcoholic sociopaths who dream of an authoritarian, fascist world dictatorship. I'm not sure how that fits the punk ethos?