... they didn't seem to give Jason White the respect or visibility I thought he deserved ...
I've thought about that, too, Tom - I imagine the mindset was they were perceived as a trio and/or conceived of themselves as a trio, so he's like that "other guy" who just happens to play on all their songs but never make it into the publicity photos.
A quick Googling confirmed that he's played with the band off and on for most of their history, and pretty much regularly since American Idiot. Finally, with this
single release last year, he got an official listing as a band member.