Something that people need to understand is that lack of empathy/sympathy does not make you a bad person, the way you react to things does. For example people with aspd often get a lot of hate thrown at them for not feeling bad about certain situations while they make it loud and clear that they have aspd and therefore have sympathy problems.
Me included, I don't have aspd, but I have a problem with my emotions where I basically only feel a really small amount of emotions most of the time and for the most part just feel numb. This has highly affected my sympathy and I just cannot care. I can still recognise that it is mean to do things and that someone feels sad, but I don't care. I do care enough to the point I cannot hurt people on purpose, because that makes me feel too guilty. But if you tell me your pet died, I don't care, I don't feel bad there is only this logical part of my brain that tells me how to react sympathetically and that they feel sad. And here's my point, I don't hurt anyone by doing this. And especially if I'm clear about this issue it doesn't hurt anyone and people are prepared.
Same thing with humanitarian crisises, I care in the sense that I know it's horrible and deserves justice, but thinking about the people affected I don't feel the actual sympathy. Again just my logical response of, this is bad, they need help, I need to do something. But the way people will jump you for not feeling bad and being honest about it is insane. And the people expierencing this cannot do anything about it.
And about the reacting thing. How you react to things does define whether you're a good or bad person, at least in that moment. But I will say if the lack of empathy does affect your ability to respond in an empathetic way, that does not count. If someone knows they cannot respond accordingly and therefore think it's best to distance from the sad person, because it's better than accidentally saying innapropriate things, then that is valid.
I'd like to add, before I get people saying it's on me or that I'm part of the problem why victims aren't being taken seriously. I've never had a big issue with this. I have no issue feeling bad for Armand, Louis, Claudia or lots of other characters in fiction. I've have felt bad for some of the most hated characters you can think of. Found sympathy for people even when they are in general still horrible people. The reason why I make this post is not because it's Lestat but because Lestat is the only one where I can't find the sympathy.