thinking in terms of Hat color isnt helpful because it presumes Mueller has 'picked a side' and is 'deceiving the other side' its more accurate to think of it like this Mueller is a crook. He doesnt know yet if Trump will prevail over the Deep state, or the Deep State will prevail over Trump. So he is hedging his bets so that whichever one prevails he has an 'insurance policy' for himself and wasnt seen to betray the victorious side too badly he's just acting in survival, and which color hat he wears shifts with the circumstances and prospects