I think it's quite sad and I hate hearing it.
I don't remember booing our own team in "the old days". We would hang our heads, get angry and go into a depression when we lost and we'd rant about it and let off steam against whichever players we thought had played badly after the game was over.
When our supporters cheer the team on and chant and sing, the players do say that it feels like having an extra man on the pitch. So perhaps jeering and booing makes them feel they're playing at a tangible psychological disadvantage. I don't think it can help.
The fact many teams will say it's important to shut the crowd up or (as I have heard about us specifically) get the fans on the backs of the players shows that this is a genuine tactic for the opposition.
It's niave to suggest it has no bearing and is usually done so by those wishing to justify their own actions. There's a common denominator here.