"the sin of empathy" has been a Christian doctrine in conservative circles for a few years (at least since 2019).
Churches with universalist doctrines were supporting social change. The Christian reactionaries did their thing by organizing themselves in opposition to this change. Some particularly conservative Baptist called Rigney decided to avoid emacipatory arguments all together and attack what he saw as the pillar concept instead: empathy. 2019 https://ghostarchive.org/archive/UXWex
Also in classic reactionary style, he was cribbing off left thought. Empathy has been a target for criticism from the left going back to at least 2016. https://en.wikipedia.org/wiki/Against_Empathy
I don't have theological opinions. But I feel like the culture I grew up in valued empathy maybe a little too much. I used to believe that people who did the horrible things lacked empathy. But that can't be a universal truth. I see people celebrating the cruelty in policies like mass deportation. You can't enjoy somebodies pain if you can't recognize it. I've also come to learn that being cruel to others can be pro-social.
Isaiah, verse 5:20, which says, "Woe to those who call evil good, and good evil; who put darkness for light, and light for darkness."
The Bible's just chock full of biting criticism and warnings against the behavior of people who pretend their hate and bigotry is a tradition they must follow.
Oh hey I'm pretty sure I've seen people people put that on signs while protesting against gay pride lol.
The problem with morality is that it's difficult and it's really easy to twist any guidelines into whatever you want, and what you instinctively want is almost certainly to feel like you're smarter and more moral than others as you are right now with no self reflection and minimal effort. If you have internal prejudices you can probably twist whatever system of morality you have into saying they're good and right and those criticizing you are actually bad.
You have to want to actually be good. And empathy is a good place to start, but listening to others about their needs and experiences is also crucial. And while you do it you've gotta remember not to prioritize the feelings of the bigot over the affected (I'll try to remember to link the contra video I borrowed that observation from)
I'm sure somewhere in the bible, there is a line to justify the lack of empathy. Regardless of factions and sects, any religious person would not be doing what they do if it isn't prescribed in their sacred text.
The entire Old Testament was about a "jealous god" going around committing genocide based on perceived slights. You can find something in there to justify any horrific shit.
It's tribalism plus brainwashing. They believe the right way to show empathy to the in-group is to attack anyone in the out-group. Driven by zero-sum thinking and beliefs around "natural social hierarchy" being necessary.