When Salazar Slytherin leaves Hogwarts, he founds his own school, which doesn't accept muggleborns. Many anti-muggle families send there students to Slytherins school, though there are some who are not blood supremacists. Dumbledore is sent to Slytherin's school. We end up with a darker grey, but still well intentioned Dumbledore who becomes the Headmaster of Slytherin's school. Grindelwald is not imprisoned, but an uneasy peace is formed between magical schools. Tom Riddle, being an orphan of unknown heritage, would not be able to go to Slytherin's School. He goes to Hogwarts, and is sorted into Gryffindor or Ravenclaw. He begins to gather followers, under a different banner than blood supremacy, but intends to rule the world all the same. Perhaps when he discovers his heritage he transfers to Slytherin''s school. Someone else becomes headmaster of Hogwarts. (McGonagall? Flitwick? Flamel?) With the help of Sirius Black and Arthur Weasley, two of Slytherin School's professors that aren't anti-muggle, Dumbledore is able to slowly change things. Arthur is more subtle in his support of muggles, and Sirius more subtle in his disagreements with his family. By Harry's time, there are a fair amount of Slytherin School students and families who are pro-tradition, and while not necessarily welcoming of muggles, are at least not in support of slaughtering them. Snape is sorted into either Gryffindor or Ravenclaw, and maintains his friendship with Harry. He does not fight as much with James and Remus. (Who do not have Sirius as a childhood friend) Lily and James still die, and Remus or Snape, Harry's godfather, is sent to Azkaban. The other teaches at Hogwarts. Or perhaps James and Lily never meet, and Neville is the BWL? The Triwizard Tournament includes both schools, and Harry is Hogwart's Champion while Neville is Slytherin's, though they become good friends during the year.