It’s common practice for an anime to feature a male lead whom the audience can easily relate to, and therefor usually holds to society’s moral compass. It’s also common practice for that male lead to have one or more female love interests, and not uncommon for one of those love interests to follow a conflicting moral compass. This creates a “Defrosting the Ice Queen” situation, wherein the lead tries to bring his love interest over to what he views as ‘the side of righteousness.’
Being as I’m at ends with society’s moral compass and have a deep hatred for self-righteous people, I’m always wary of this trope. However, surprisingly, I often find it to be justified. For example, take Revy, the Ice Queen from Black Lagoon. The male lead, Rock, tries to change Revy and create some sort of moral base within her, but he does so because her attitude and actions are self-destructive. He gradually admits that while he doesn’t approve of her criminal way of life, he understands it, and he makes it clear that he wants Revy to change for her own sake, so that she can find happiness instead of wasting her life.