While Salazar wanted to teach only students from magical families, some halfblood families (like Harry and Tonks' families) probably met his criteria. Yes, Malfoy makes a lot of loud-mouthed remarks currently, but I can't see the Sorting Hat deciding to offer Slytherin to only two halfbloods in a century. It would stuff too many students in the other dorms, for one thing.
Normally, belief systems tend to change over time to fit new circumstances. Salazar lived a thousand years ago, and since then, as Ron quite rightly points out in this book, almost no one is 100% pureblood anymore. I suspect that the criteria for Slytherin house became less rigid as the "purebloods only" demand became less realistic. Then, as sometimes happens, there was a fundamentalist backlash against the change, popularized and mobilized by charismatic leaders (Tom Riddle, certainly -- maybe also Grindelwald).
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Normally, belief systems tend to change over time to fit new circumstances. Salazar lived a thousand years ago, and since then, as Ron quite rightly points out in this book, almost no one is 100% pureblood anymore. I suspect that the criteria for Slytherin house became less rigid as the "purebloods only" demand became less realistic. Then, as sometimes happens, there was a fundamentalist backlash against the change, popularized and mobilized by charismatic leaders (Tom Riddle, certainly -- maybe also Grindelwald).