Two things I don't fall for in fanfiction:
1. When they turn Ron Weasley into an ignorant fool who only knows how to yell, get angry, and be jealous. Bashing Ron Weasley is one of the most senseless things in the world. It's never, and I repeat, it's never necessary to turn Ron into the villain for the villain to achieve redemption (usually it's Draco). To me, it's always a sign of the author being lazy and wanting to make everything too easy for their story.
I'm sorry, I just can't believe that someone who's so good at chess is too dumb to understand human interactions, or plans, or anything else. Turn Ron into a monster, separate him from his friends, having any kind of Weasley Bashing is enough for me to know that I'm not going to like that fanfic.
2. When any Slytherin simply stops believing in blood purity. It's not about changing their mindset, but about how easy it is sometimes. I don't buy it. When they are the biggest advocates for the cause, yeah no. Anything we learn as we grow up takes root, and it's not so easy to unlearn. Sometimes it's impossible. For example, catholicism. It's been almost a decade since I left religion behind and I don't believe in anything, but I'm still terrified of thinking the wrong thing and going to hell. I consider myself agnostic because the thought of believing with conviction "god doesn't exist" terrifies me, deep down. Out of fear of going to hell, and I don't even believe in hell.
So no, the Slytherins wouldn't simply leave behind years and years of a way of thinking that was instilled in them from birth. They would still say prejudiced things from time to time, they would still think about it and would have to constantly remind themselves that it's wrong. Or that they're not like that anymore. But sometimes in fanfics, they're simply able to have relationships with Muggleborns and have Muggle experiences, or coexist with Muggles. Very easily. Yeah, I'm not buying that.