The real problem for Chelsea is not opposition fans criticising 'from a distance', it is their own fans damaging the their club from within. In fact Chelsea fans are acting like opposition fans at the moment. The more they boo and jeer, the more turmoil they create and the more they help Arsenal and Spurs.
Avram Grant was given as tough a time as Benitez yet the team still went on a good run, also the away form has been just as bad as the home form (actually worse) under Benitez so I don't think it's as clear cut as to say the fans are damaging the club.
I think neither but I think the sacking of RDM has damaged morale in the dressing room which has invariably led to a dip on form. In the past Chelsea managers have been (allegedly) sacked for i) huge dip in form/lowly league position ii) Fall out with the players. In the case of RDM it was neither, he was very much liked by the players and staff in contrast to Benitez who clearly isn't. Nobody to blame but Abramovich and primarily the board.
Neither helping nor hindering ? I can guarantee you that the players will be affected by the turmoil your fans are creating. You might hate Rafa, but his players are playing for him and the schism that your fans are creating between manager and players is not helpful at all. The trouble at Chelsea is that Roman is an autocrat with all the power, he bankrolls the club and therefore he calls the shots. the fact that he's sacked so many managers in the last few years has gone unchecked is worrying. When he sacked Mourinho, people should have been asking questions. But he has almost become untouchable, because you rely on his money. No Roman, no money, no success. It's a classic case of having sold your soul to the Devil.
Not the full formula, to equal success you also need a top manager, they had this with jose but f*cked it up.