Molly Weasley, a Gryffindor, may have been a bit prejudiced.
When Ron meets Harry for the first time, and Harry asked if his family were all wizards, he says he thinks so but his mother might have a second cousin who’s an accountant. Since he says this in response to a question about if his family are all wizards, this implies that the second cousin has no magic, and isn’t simply a wizard with a passion for accounting.
“Are all your family wizards?’ asked Harry, who found Ron just as interesting as Ron found him.
‘Er – yes, I think so,’ said Ron. ‘I think Mum’s got a second cousin who’s an accountant, but we never talk about him.”
- Harry Potter and the Philosopher's Stone, Chapter 6 (The Journey from Platform Nine and Three-Quarters)
This doesn’t really indicate prejudice on Ron’s part, since it wasn’t his decision not to talk about this relative. However, it could indicate that his mother found having a second cousin who was a Squib or Muggle shameful enough not to talk about. It’s most likely to be his mother who made the rule, since it’s her relative, and Arthur Weasley absolutely loves Muggles - he certainly wouldn’t want to keep quiet about being related to one.
In addition, whoever made the rule would have needed to have some authority over what the family talks about. Ron’s brothers wouldn’t likely have that sort of authority over the family, especially if their mother disagreed with their opinions. It’s possible that the reason they never talk about the accountant second cousin is unrelated to prejudice, but from what Ron says, it certainly seems to be as a result of him not being a wizard.
All of the Weasleys, including both of the Weasley parents were in Gryffindor, so they were explicitly not Slytherin.
“What house are your brothers in?’ asked Harry.
‘Gryffindor,’ said Ron. Gloom seemed to be settling on him again. ‘Mum and Dad were in it, too. I don’t know what they’ll say if I’m not. I don’t suppose Ravenclaw would be too bad, but imagine if they put me in Slytherin.”
- Harry Potter and the Philosopher's Stone, Chapter 6 (The Journey from Platform Nine and Three-Quarters)
Ron in fact thinks it’d disappoint him parents if he’s in any other house than Gryffindor, and sees being in Slytherin as the worst. The Weasleys were not only not Slytherin, but they may have been actively opposed to Slytherin, given Ron’s reaction to the idea of being sorted there.