This booing and confidence issue doesn´t make sense. As a Sporting fan and season ticket owner, i can tell you that the same thing happened when Nani played for us. Nani was a great player for us and most of the Sporting fans miss him now but i clearly remember him being one of the most booed players. I don´t think it affects him. What affects him is form and a decent run of games, manager trust and things going his way at the beginning of the match.
When Nani gets going, he was one of the best players in our history but since he is a winger and an avid dribbler, he is capable of infuriating even the most patient fan when things aren´t going his way. Nani´s decision making was also a problem at Sporting (he has evolved at United) although he was the player with the most assists. Fans notice his flaws instantly because he was always on the ball and trying to create something.
People were pleased when we did the 25 million deal, the problem is that we only noticed how good and influencial he was for us when he was gone and there was no one left as dangerous and productive to create. Sporting fans also had the same Love/hate relationship with Nani. I clearly remember the epic Nani threads on our forum. Same thing will happen if he moves to Juventus or any other club.