I'm a ST holder, and though I'm sick of Lambert and would happily welcome a new manager, whenever I hear chants of 'We want Lambert out' or booing, it just makes me want to sing the usual supporting songs even louder, and often over the top of the people showing their anger.
People like me will just see negative chants as counter-productive when they're sang during a game, while your team is trying to defend/build and attack or (unlikely) score a goal.
I don't agree with worrying too much. If the players feel valued by the fans then I doubt a song or two against the manager will have any negative affect on them. I doubt it'll hinder our attack or defence if the fans are singing "We want Lambert out". If a negative song or two, not even about them, is belted out once in a while, and it really does impact them psychologically then I'd seriously question their mental strength for playing top level football. I don't remember this much fan restraint in giving what for during the final days of McLeish.
It is mystifying. It's almost as though fans lambasted McLeish just because he came from SHA and not for his competence as a football manager. I hope that is not the case as it would suggest a level of small mindedness.
Welcome to Aston Villa!