I think the only reason they change/mess with the tunnings is making interesting to play them. The change comes from the very early days. The first eps are in D standard, the first LP are in E standard and Kerplunk are in something close to a Eb tunning but is not exactly that. Even so, they did shows in E standard in 93, and some in D in 92.
In 98 they did Dominated Love Slave in E standard
In the 2000 they played Brat in standard several times and Blood, sex and booze in Eb
In 2001, Castaway had a fixed slot in the setlist and it was played in E tunning
Around 2009, BJ played several song with changed keys, for various reasons, like it was easier to play with open chords, or the guitar on hand was in different tunning. Examples would be Give me novacaine, No Pride or Tight wad hill.
2010 had a lot of songs played with Blue since they had a old school section with only Eb instruments. Songs like Platypus, Scattered or Waiting were played with Blue.
In the trilogy era, they had a crush with sounding garage-y so they played in standard a lot. Basket Case, Longview, Hitchin', Welcome to Paradise and Burnout were played half step up
In revrad, they used to stick more to the original tunnings, but they were playing a modified version of waiting where they put the song half step up so it can be played with open chords. Also the Les Paul Jr used by BJ in American Idiot and Jesus of Suburbia is on Eb, so he can play them with open chords and reach a lower Eb chord that is present in both songs, creating a different mixing of the guitar sounds.