This is my view, more or less (though one could legitimately argue that bidding to build one's first ever private datacentre for the CIA is a much closer relationship than simply not preventing the CIA from having AWS accounts). Selecting a board member whose most relevant achievements are circumventing security legislation and browbeating foreign governments (she's undoubtedly extremely smart but she's not been appointed for investment or engineering insights) says a lot more about a company than whose cash they'll accept.
That said, the many calls to boycott Amazon were perfectly reasonable too.
Rice: Dropbox's board member
I don't think "pitchfork mobs" would object to Rice merely being a customer, even if she stored documents for objectionable purposes.