Mate you're looking at it the wrong way, it's not about him leaving, no one expected him to stay if Rangers were relegated, no one would hold that against him, the reason he is hated at Ibrox is because of the way he went around it. Naismith was known as a self proclaimed Rangers fan, talked about how glad he was to be playing for his boyhood heros and then;
1) he chooses to not sign onto the Newco even though it was clear he would have been allowed to be sold off, but instead he left without the contract so he will receive a nice big sign on fee at Goodison - Rangers fans would have been happy with 1m for him.
2) in his press conference the self-proclaimed Rangers "fan" stated he owed nothing to this club as "The Rangers" (oldco) no longer existed and he had supported the oldco and played for them, he wouldn't call the newco Rangers (which they are) so he could distance himself.
He is one hundred and twenty percent a class a rat. Imagine a player being so glad to be at Everton as they were his "boyhood heros" and then Everton get liquidated and he runs off to get more money for himself and says that Everton don't exist. That's why the fans hate him. The fans are angry at Davis, but not as angry because he didn't make any statements like that.