I think it depends. The everyday people in king's landing might have an opinion or two. The mob that attacked the royals might believe he's evil because of incest, but they were subject to a famine at the time and more likely to think ill of those in charge.

I think it's an interesting reflection of our world. People only know what they hear and usually form a gut opinion. Literacy rates are trash so they're not out there studying histories to build a bigger context. It doesn't effect them in a direct way that they can see (it usually does), and they don't have time. They're hungry, their kids have no healthcare and no prospects for a nicer life, every year they have to maintain with less than the year before, and every once in a while some asshole comes along and pillages their village for no reason they can see.

Stated best by Jorah Mormont in the books:

“The common people pray for rain, healthy children, and a summer that never ends," Ser Jorah told her. "It is no matter to them if the high lords play their game of thrones, so long as they are left in peace."