This is my full question since I couldn't fit it all in the title:
How different would the Harry Potter series be if the Head of Slytherin House was a strict but fair person who also doesn't believe in blood purity while Snape was just a Hogwarts teacher and a member and spy of the Order of the Phoenix?
If there was a different Head of Slytherin who was jovial and cheerful and a pure-blood supremacy hater, things could easily turn out well for the school, students, staff and trio.
And things wouldn't be too different either.
A fair Head of Slytherin would have reigned in Draco Malfoy and his lackeys. Draco’s outbursts such as “You’re next, mudblood!” would likely have netted him in detention. This would in turn have kept Harry more level-headed. A Head of Slytherin who didn’t support blood purity would probably not have gotten along at all with Lucius Malfoy.
The Quidditch outcome probably would’ve ended up the same, possibly worse for Slytherin; it might be that Lucius would’ve refused to sponsor brooms for the team if there was any chance of “blood traitors” on the team.
During the Reign of the *****, Slytherin would probably have had less of a favoured position, and some of the Slytherins might’ve been invited to join Dumbledore’s Army.
In general a more fair Head of Slytherin who made it clear that they didn’t believe in blood purity might in the longer run have served as the catalyst needed to build the unity a Hogwarts that the Sorting Hat famously sang about.
If Snape’s behaviour in general was the same things wouldn’t change much for the main characters though. Harry would still get a lot of detentions (both deserved and undeserved), he and Neville would still be treated unfairly in potions, Hermione would still be ridiculed by Snape, etc. The twins would still get just as many deserved detentions.
(MoM Edit: Removing profanity)