Why did Nancy forgive Steve even after he called her a slut?

Because this was an age before the notion of “slut-shaming” came into vogue. Nowadays calling a woman a slut might be an unforgivable thing, because in the feminist view you are oppressing women by casting moral judgment on their choices.

But in the 1980’s, the word was more common. It was still not a nice thing to say, but that’s just because to be promiscuous and “easy” was thought of as a bad thing, so being accused of that was bad because you were being accused of bad behavior, not because it was misogynistic or anything.

So while Nancy was angry that Steve was accusing her of cheating on him, it was the kind of thing you could forgive if the person later realized that you weren’t promiscuous and apologized for falsely accusing you. It wasn’t the kind of word that revealed that the person speaking it was fundamentally bad.

Steve redeemed himself by protecting the younger kids and staying to help fight the Demogorgon.

One of the most refreshing things about Stranger Things is the fact that they don't doggedly stick with people either being BAD or GOOD, but instead treat them like actual people. Yes, Steve was a selfish jerk and outright cruel sometimes. In most entertainment, this is a clear indicator of him being a bad guy--full stop. But in real life it just means he's a teenager struggling with his own insecurities and hormones. Instead of making him an irredeemable villain, the show makes him human and shows him feeling bad about what he did. It also shows that when push comes to shove, he's not that bad a kid and can act to protect the younger kids and stick it out to fight the Demogorgon, even though Nancy and Jonathan gave him a pass to get out of there.

So when Will is back and the monster is seemingly defeated, Nancy reevaluates Steve, finds she still has feelings for him and is attracted to him, and forgives what he did and stays with him. Remember that they were in a relationship before he acted like a jerk, so those feelings were all in place--and Nancy's a teenager too. Sometimes when you really like someone, you forgive them for hurting you, especially when you're a teenager.

This theme of the person who acts like a jerk, or even a villain, but is redeemed can be seen elsewhere in the series. For instance, Billy is a very cruel and self-absorbed person and it's even hinted that he is that most heinous of things in our society: a racist. And yet in Season 3, Eleven discovers that Billy was once a pretty good kid who just got hurt and twisted by a mean father. And in the end, Billy acts the hero and sacrifices himself to save everyone. There's also Dr. Owens (Paul Reiser's character) who goes from being the leader of this ominous scientific program to a good guy who is genuinely concerned with Will's well being and helping Hopper with Eleven.