Keane was constantly haranguing his teammates, demanding the best of them on the pitch and even in training. It's what made him a great leader, and although they all no doubt respected him I wouldn't be surprised if it annoyed them as well.
It might not be in entirely the same vein, but from what I've seen of Bruno he's a winner who tries to give his all and expects his teammates to do the same. It's something we've sorely lacked, and it's no wonder our overall performances have improved since he joined.
Exaggerating pain is just part of the modern game unfortunately, especially in Italy Portugal where he played before. He doesn't even do it that much compared to a lot of players, especially as he does find himself targeted for physicality now, so you're just buying into the shit opposition fans have started to talk to try and discredit his ability as a player.
And, honestly, why would that annoy his teammates? As many have already said it's what gives him an edge, and we need that now more than ever.