Empathy has indeed been hijacked by a godless culture, like so many other things. The point I'm making is we need to do as Scripture commands, love our neighbor- weep with those who weep, rejoice with those who rejoice, etc. We need to fulfill the Great Commission, preach the Gospel, and teach people to obey all that Christ commands. We don't need the godless culture to tell us how to do these things, Scripture is sufficient.
What some would have us do is sin with those who sin- bear false witness and use the preferred pronoun of someone rebelling against God's created order, affirm homosexual marriage, etc. That's the warning going out about empathy.
Too many people profess Christianity and are led by their feelings into sin and conform to the world.