Slytherin, Purity, and Cunning
I'm wondering whether Salazar meant "pure" the way purebloods do today. According to the Online Etymology Dictionary, the word "pure" wasn't used in reference to bloodlines until the late 15th century. Before then, "pure" was used in reference to one's soul. To be "pure" meant that one was free from moral corruption. Therefore, perhaps when Slytherin said that he wanted students "whose ancestry is purest," he meant that he wanted students from morally upstanding families.
Another possibility is that Slytherin was concerned about "purity" in terms of how one performed magic. Jodel has a great essay on the history of magic in which she suggests that the distinction between "dark" magic and "light" magic was originally one of "old" magic vs. "new" magic. The use of old magic was both dependent upon and affected the state of one's soul. New magic became popular because it was considered safer and less likely to drive one insane. Perhaps, then, Salazar considered new magic to be less "pure" than old magic because the state of one's soul didn't matter so much when using new magic; it didn't matter whether you were pure of heart in your intentions. We know that Slytherin House draws students who are interested in the "dark arts," so maybe Salazar was looking for students who came from families that still followed the old magical traditions rather than using those newfangled spells that were being invented at the time.
Slytherin may have also meant something different by "cunning" than we do today. In medieval and early modern Britain, a distinction was made between malevolent witch-craft and benevolent folk magic. The practitioners of benevolent magic were called cunning folk. Cunning folk performed services such as protecting against malevolent witch-craft and healing. Their practice of magic was entirely legal until the mid-16th century, and they practiced openly in their communities.
If these possible meanings of "pure" and "cunning" are at all correct, then I don't think Salazar's concerns had anything to do with admitting muggle-born students.
ETA: The sorting hat actually specifically uses the phrase "cunning folk" in its song in PS.
Another possibility is that Slytherin was concerned about "purity" in terms of how one performed magic. Jodel has a great essay on the history of magic in which she suggests that the distinction between "dark" magic and "light" magic was originally one of "old" magic vs. "new" magic. The use of old magic was both dependent upon and affected the state of one's soul. New magic became popular because it was considered safer and less likely to drive one insane. Perhaps, then, Salazar considered new magic to be less "pure" than old magic because the state of one's soul didn't matter so much when using new magic; it didn't matter whether you were pure of heart in your intentions. We know that Slytherin House draws students who are interested in the "dark arts," so maybe Salazar was looking for students who came from families that still followed the old magical traditions rather than using those newfangled spells that were being invented at the time.
Slytherin may have also meant something different by "cunning" than we do today. In medieval and early modern Britain, a distinction was made between malevolent witch-craft and benevolent folk magic. The practitioners of benevolent magic were called cunning folk. Cunning folk performed services such as protecting against malevolent witch-craft and healing. Their practice of magic was entirely legal until the mid-16th century, and they practiced openly in their communities.
If these possible meanings of "pure" and "cunning" are at all correct, then I don't think Salazar's concerns had anything to do with admitting muggle-born students.
ETA: The sorting hat actually specifically uses the phrase "cunning folk" in its song in PS.