Barca and Madrid fans are used to success. The older ones are also used to the way it comes and goes. They're also used to gloating when the trophies are going one way and the club politics is turning the other lot into a circus. It's good for a laugh. They also know how it works, because they remember when it was the other way round.
However, there are already a set of Barca fans who don't remember a time before Guardiola. They "remember" because they've read about Madrid sacking Del Bosque. They don't "remember" booing Rijkaard and his team two years after they won a CL/Liga double. They don't remember Cruyff winning 4 Ligas in a row, and a European Cup, and getting booed and sacked after two trophyless years.
The pressure on Tata now is coming from the catalan media. They've been meticulously supportive of Barcelona for the past few years; completely different to how Marca/AS treat Real Madrid. Now the negative stories are leaking out: about the players their form, fitness and attitude; the style of play and even about Messi. Some of it seems to be coming from inside the squad. Tata's in the middle of that and a focus for discontent, and Rossel cares only about self-preservation.
People laughed about Raul's role at Madrid, probably endowing him with more (malicious) influence than he actually had. Now the Madrid fans are watching with amusement as players like Xavi get charged with being "too big to drop" and Tata's taking the hit both for choosing him, and for taking him off.
So the fans then. Yes the big two have their shares of idiots, arrogant prats, clowns, and perfectly normal fans. The ratios in my experience tend to vary from year to year, decade to decade. Not that different to United fans really.