Some people believe that conservatives lack empathy for others as a result of their tendency to not believe something until it affects them personally, which is a statement that would likely get a lot of flack if it were asserted on conservative forums. Now, I don't necessarily believe that they lack empathy, but who they show empathy to is highly subjective. Veritasium did a video on "Is Success Luck or Hard Work?" and I believe that conservatives believe that success is primarily due to hard work while liberals believe that luck plays a more significant role. Therefore, if a person subscribes to the "hard work leads to success" world view, any faults or issues in someone else's life is a result of them making poor decisions or them not working hard enough. Conversely, when someone has success in their life, they believe that it must have been entirely due to their own decisions, regardless of what natural advantages were afforded to them purely due to factors outside of their control. This concept is what conservatives call "personal responsibility", that humans are in control of and decide their own outcomes.
Going back to the topic of empathy, when conservatives don't believe something is happening until it happens to them, it's because they believe that when it affects someone else, it's because of that other person's own fault, which is the "It's your problem, not mine" or "Fuck you, got mine" mentality. Conservatives don't believe that racism or other inequalities are an issue because they aren't negatively affected by it. However, any benefits granted to them by being white or privileged they associate with their own inherent "talent" or "hard work", even though it wasn't something they had control over to begin with. I believe that when conservatives are empathetic, it's usually to those who get a natural advantage taken away from them, i.e. when privilege is taken away from someone who enjoys that privilege, it feels like unfairness to the person because they "worked hard" and "didn't deserve it". You can apply this to taxes, healthcare, welfare, social rights, etc.
Conservatives feel like they shouldn't be taxed more because they worked hard to earn their money, even if it was made through accumulated generational wealth. Conservatives feel like they shouldn't have to pay for other's welfare because they don't see themselves as needing to rely on it, yet others are using it, even though the people who depend on it may not have the same privileges afforded to them, which would help them get off welfare. Conservatives feel like LGBTQ people shouldn't be granted the same protections because they believe that being LGBTQ is a choice and not something that was outside of that person's control. Anyways, the list goes on and on.
Well, I agree, except I think that "who they show empathy to is highly subjective" (probably should be "highly selective", no?) applies to everyone, not just conservatives, and it's part of the limitation of empathy. It's why empathy is a bit over-rated as a trait, and why it's not sufficient to base any sort of social system on.
I think everybody finds it hard to empathise with those who have had very different experiences to themselves, or who exist in very different circumstances.
Also, everybody wants to believe their good fortune is due to their intrinsic virtues. You see that all the time, in all sorts of different contexts, it's the underlying basis of victim-blaming.