Question about Pure Bloods and House of Slytherin

[potioncat]

Kemper wrote: 
> If Mr. Filch thought himself to be Pure Blood (or Half-Blood for 
that matter), he wouldn't care what was written on the wall, only 
that Mrs. Norris was petrified and hanging underneath the foot high 
words.
> 
> It's not his lineage that Mr. Filch cares about, it's his inability 
to perform magic which makes him like a Muggle, an enemy of the Heir.



Potioncat:
Canon fire starboard bow! Good shot.
<loading own can(n)on while bailing water>

DH, chapter 1. We have LV ranting at the very idea of Wizarding kind 
marryin Muggles. Yet, at LV's right hand sits an offspring of just 
such a union. 

I have no doubt that LV would not deal kindly with Eileen Snape, 
should he have reason to come in contact with her, yet he accepts her 
son. So I would think a child of a Squib/Wizarding union would be 
accepted.

On the other hand, if the child of either of those matches was in 
full support of his non-magical parent, it might be a different 
situation. Though, we don't have canon for how Snape describes his 
father to his Slytherin friends.