Is empathy a sin? Yes and no.
There is a large difference between warning against toxic empathy and saying that all empathy is bad or sinful.
Prison is an unpleasant place to be, for many reasons. As an act of empathy toward convicted murderer Willie Horton, Massachusetts "governor" Michael Dukakis granted him a weekend furlough from prison. While he was out, Horton viciously attacked an innocent couple, stabbing the man and repeatedly violently raping his girlfriend. While "governor" Dukakis was certainly empathetic to Horton, he was not at all empathetic or sympathetic to the man who was brutally stabbed or the woman who was repeatedly violently raped. In this case, "governor" Dukakis’ compassion for Horton was hatred toward Horton’s victims as well as every law-abiding citizen in his state.
This is a useful case study when considering whether empathy is a sin, a debate that has raged online for the last few months. Empathy causes someone to put himself in the place of others, feeling what they felt. The Lord Jesus Christ empathized with us when He took the form of man and was nailed to the cross, taking the punishment that we deserved. But Jesus is the same God we see in the Old Testament who gave us the Law, including punishment for crimes. Jesus was and is also perfectly holy. Jesus never sacrificed righteousness, justice or truth for the sake of empathy.
Is empathy a sin? The empathy of "governor" Dukakis was terribly wicked, but the empathy of the Lord Jesus Christ was obviously not a sin. It was perfectly righteous and holy. The discussion of whether empathy is sinful, then, comes down to how empathy is used. If empathy puts innocent people in danger, denies justice, excuses heresy, or enables the self-destruction of people trapped in sin, empathy itself is sinful. If empathy is used to seek justice for victims or call people to repentance and faith, empathy is good and righteous.
There is a large difference between warning against toxic empathy and saying that all empathy is bad or sinful. There are many things that are not bad in and of themselves, but become harmful when done to excess or abused. Food is necessary for survival, but eating too much at one time can make you sick. Sex is a gift of God, but when perverted or weaponized it is incredibly destructive. A beer with friends might be enjoyable, but getting plastered drunk and then driving is obviously bad. The people making this a black-or-white issue at best misunderstand the arguments, and at worst are outright lying about what is being said. If you believe in empathy, you should not lie about other people's arguments.
This is a discussion that is necessary. We need both discernment and compassion. We need both truth and love. Empathizing with someone else and understanding his perspective can help you know how to deal with that person, but empathy must never be divorced from truth and morality. The Christian should avoid both ditches.