I think in the Dookie days Green Day was in the punk era. Then it faded to pop punk. It's still that. They haven't changed their genre since then.
They've been grilled on it in interviews, but they've always said that punk is really just a state of mind, and they've always kept tat. Around American Idiot, they weren't pop punk, they were harder than that. But still not complete PunkRock. Not like The Sex Pistols.
(Keep in mind, I am listening to them as I write them)
Green day, in my opinion is the epitome of what punk rock should be. From Kerplunk all the way down to Tre, they have upheld the high standards of what punk rock truly is. Sure, they may have turned to more pop sounding instrumentations, but they have still held the integrate pop into it. Albums like American Idiot is what has revolutionized modern punk.
Green day was more pop punk than punk. They had some good songs that could have been considered punk such as American idiot or working class hero, among other earlier songs. But as of late, they moved away from the punk scene to more pop sounds. They're not rancid or rise against, but they're close.