Not sure how well he would be excepted by the Los Blancos public they are pretty tired of the Mourinho brand of anti football. Rafa is also seen as a proponent of this style, he even has a nickname in Spain for the type of football he plays "The Italian" Real fans want a return to their swashbuckling ways, Capello & Mourinho in particular left and will leave on bad terms with the fans because they didnt give them that, despite landing them La Liga titles. What could work in Rafa's favour is his record in European competition, they badly want that tenth trophy.
In terms of football style, you are right that the Real Madrid fans would prefer attacking football. Mourinho's defensive counter-attacking football was not very popular with them. While they may not be overjoyed at first with Rafa's tactics - he plays balanced football and his first priority will be to sort out the defence - I think that they may be quite happy after a few months. With the right players, Rafa's team can play very entertaining football. Real Madrid fans surely still remember the 4-0 beating of Real Madrid at Anfield - that was an example of winning attacking football.
Mourinho's problems at Madrid runs deeper than just the football style - he has criticised the fans, he has behaved a certain way that is not compatible with the Real ethos, he has provoked an internal war with his most influential players (this has been going on for 3 years) and he has continously said that he wants to leave.
Contrast that with Rafa, he grew up as a Real Madrid fan, he was a youth player there, he coached their youth teams and second team. Morever, he was assistant manager to Del Bosque for a brief spell at Real. After 3 years of Mourinho, Rafa would probably be welcome as a saviour of Real's image (even if the fans may not be totally overjoyed with the football style).
After dealing with Chelsea fans who initially hated him (many still do but many now grudgingly respect him), dealing with Real fans will be a piece of cake. If he succeeded to silence Stamford Bridge, then managing at the Santiago Bernabeu and getting the support of the local fans will be a breeze.
As a side note, I would have been interested to know how top managers like Guardiola, Mourinho, Capello, Del Bosque, Pellegrini, etc or even Ferguson would have managed in the same situation like Benitez did - with fans continuously booing them at home and then travelling to away stadiums to boo them as well. Of course, we would probably never know since it would be virtually impossible to recreate an atmosphere as toxic as Stamford Bridge.
