From a personal perspective I would never boo a blue in my life, nor offer overt criticism at a match.
Sure I might get frustrated but I see my role as a spectator and supporter as one of encouraging the blues and making life as difficult as possible for the opposition by giving my full support.
The act of booing at half time can only encourage the opposition, an act that their management would use against us in the half time talk.
If you must boo, boo at the end of the game when you can no longer influence the result, better still support our team regardless of performance, managers tactics and/or the ineptness of the Board.
Make your protests outside playing time.