Hardly. Regardless of who you side with, mages, as a group, are seen as responsible for blowing a hole in reality, starting a war that saw innocent people in the Hinterlands ravaged, and getting Redcliffe taken over by Tevinter Magisters. Yes, they find some redemption if they assist in closing the Breach, but that's hardly going to sway people who hold them responsible to begin with.
First the whole was made by Corypheus
Second Redceliff was raided by Templars and the majority of death toll were the people of redcliff
Third The mages didn't just close the breach. They fought Corypheus, protected people from Red Templars who were using people as red Lyrium mines, They stopped a demon army, and everything else the Inquisition did. Mages and Templars based on who you side with form the majority of the armies of Inquisition.
Plus, we still have a thousand years of anti-mage bias that has completely shaped the cultures of Southern Thedas. That's not going to just 'go away', regardless of how much good mages may or may not have done during a magical crisis that threatened the world. And even if most mages are kind and benevolent, all it takes is one or two like the idiots running rampant through the Hinterlands proclaiming their superiority and throwing around fireballs to sour relations with a population already predisposed to view them with fear and hatred (and that doesn't even start to address the common view when little Timmy sneezes and burns down the farm).
People listened to Justinia when she said Mages are not to be blamed for starting the war, or you'd have people killing mages all over. People put the word of the divine above everything else. Now Leliana is divine and she will tell them the same. The Witch burning and heaven selling which lasted for centuries was dissolved and went away forever in mere 50 years of renaissance. If anything people will know that circles spectacularly failed and Templars were corrupt to the core, controlled by another corrupt group (Seekers). This disaster wakes people up, if nothing else. And if they are going to rebel they will do so if old systems come back, see Vivienne as Divine who gets one rebellion after another, no one is happy with her nor her reforms aka going back to the old system.
All it would take is a group of folks unwilling to accept the College of Enchanters (or the new Inquisition) as an unbiased arbitrator of magical justice and some disgruntled former Templars and you've got yourself a nice group of anti-mage vigilanties rolling around Thedas stirring up trouble and dispensing their own take on appropriate measures.
Leliana is immediately going to get the support of common people. The first thing she does is helping the helpless, poor and those who are oppressed. She turns chantry into a charity, offering actual aid unlike the previous chantry that offered nothing but palliatives and superstition "side of the maker when you die". Do you think they will turn against their savior over some skittish tarts who think all mages are to be blamed for crimes of very few? Specially after closest people to them were saved by mages from becoming living Lyrium mines? Please find a proof for your pure speculations, hyperbole and headcanons because all you do now is rant without anything to back it up.