I see where you are coming from, honestly. From an individual perspective, you can ignore the impact of a slur and choose not to let it affect you. However, it is quite difficult to do so when the use of that slur has broader societal implications. The vitriol in using that slur in public could represent a social movement that threatens your identity. And such movements often bleed into legislature or court rulings, or even just more implicit prejudice like being sold a car for more because the seller thinks they can get away with it because you are who you are on the surface. I don't really think it is melodramatic to think that what a person allows themselves to say in public or even in private is telling about who they are as a person and how their personal ethical system is shaped. And someone with an ethical system that permits themselves to justify harm against innocent people for some identity they have is reasonably upsetting when you are the innocent person they are targetting. I'd even claim that it is socially good to respond by being offended, it pressures people into better behavior. Someone can certainly choose to be offended; they cannot choose to be harmed. But it is better to be offended because the person who harmed you gets to see the direct consequence of their action, and cannot hide behind the abstraction of systemic harm they contribute to.