Salazar Slytherin was one of the Four Founders of Hogwarts, best friends who decided to start a magical school, recognizing the need to pass on their vast stores of knowledge to future generations. Salazar was a Pureblood, and seemed to think that only Pureblood children should be taught at Hogwarts, as Muggle-borns and half-bloods weren’t worthy of learning magic. This naturally caused great friction between the four friends, especially Salazar and Godric, and he eventually left the school for many years, only returning late in life to make amends and reconcile with his friends.
The other three Houses always seem to have the worst opinion of anyone in Slytherin House, but what they all seem unable to grasp is that not all Slytherins are bad, just as not all Gryffindors are good, Peter Pettigrew being a prime example of this last statement and Regulus Black being a prime example of the first. Regulus was raised by Pureblood elitist parents, who at first supported Voldemort one hundred percent, believing he had the right idea about Muggle-borns and half-bloods. Naturally this skewed Regulus’ worldview to the point where he proudly became a Death Eater at sixteen, only his mistake when it was too late to back out. Nevertheless, Regulus redeemed himself by stealing Salazar’s locket from the cave where Voldemort had hidden it, giving his house elf Kreacher orders to destroy it as soon as he got home, then he sacrificed himself in an effort to atone for his mistakes. Of course we all know that Kreacher was unable to destroy the locket, and that the Horcrux inside it survived until Ron destroyed it years later.
Regulus was only one of many Slytherins who were not inherently bad, but who instead made bad life choices and ended up paying for them later, sometimes with their lives as Regulus did, others ending up in Azkaban. The only real requirement for being Sorted into Slytherin seemed, for the most part, to be that the student be a Pureblood like Salazar. However, we know that there were at least two half-bloods that were Sorted into Slytherin House—Severus Snape and Tom Marvolo Riddle. So clearly just being a Pureblood isn’t always the most important factor in being Sorted into Salazar’s house. That’s because the other traits he valued—cunning, a healthy sense of self-preservation, resourcefulness, determination, and a firm belief that some rules were made to be broken. (Did no one ever wonder who put all those secret passages into the school? I bet Salazar was responsible for at least some of them!)
Everyone assumes that students like Tracy Davis, the Greengrass sisters, Millicent Bulstrode, and a few others also held Salazar’s Pureblood elitist beliefs, but that’s never clearly stated in the books. Okay, so Millicent and Hermione fought during the so-called “dueling club” second year, but how much of that was Millicent honestly holding those beliefs and how much of it was her following the crowd because Draco was clearly in charge of the Slytherin students as long as he was at school? The same could be said for any of the others. Their sense of self-preservation would have kept them from calling him and his cronies on their behavior (as well as not being total idiots), but that didn’t mean they were Dark wizards in the making, it didn’t mean they would become Death Eaters once they left school, it simply meant they had the good sense to keep their heads down while they were inside the school’s walls.
I think Salazar would have approved of this attitude, and been appalled at his descendant’s. Even though he considered anyone not a Pureblood to be unworthy of magical training, I think he was pragmatist enough to realize that, like Hagrid told Harry, if Purebloods didn’t intermarry with Muggles, the wizarding world would eventually die out. He may not have had much use personally for Muggles, and it’s doubtful he would have willingly procreated with one, but he wasn’t an idiot and knew they were necessary for the continuation of the wizarding world. Of course old Tom would have a fit if anyone suggested such a thing to him; in his eyes, his precious ancestor would never allow such a thing to happen. (But I’ll tell you a secret about Tom Riddle: he was nuttier than squirrel poo.) Of course I could easily be wrong, I don’t think there’s any clear indication in canon that Salazar actually held those beliefs at any point in his life, but it’s at least a theory, something to think about when you have nothing better to do than discuss the Pureblood elitism that permeates wizarding society.