A note from isync's web site:
isync can be integrated into Mutt fairly easily with a few hooks:
folder-hook ~A bind index $ <sync-mailbox>
folder-hook +maildir 'macro index $ "<sync-mailbox>!isync -e maildir\n"'
where maildir is the name of the local mailbox (or its alias). This works well
so long as you are not modifying the IMAP mailbox outside of Mutt. However, if
you are using another mail program simultaneously Mutt will have the wrong idea
of the local mailbox flags and messages will start disappearing from its index
display (don't worry, they are still on disk).
