I don't think the usual use and denotation of empathy carries the connotations that some folks think it does. When I look at the usual reportage in the dictionaries, I'm not seeing much of anything that suggests 'endorsement' of other folks immorality or sin---or whatnot--- as a part of that disposition.
the action of understanding, being aware of, being sensitive to, and vicariously experiencing the feelings, thoughts, and experience of another; also : the capacity for this… See the full definition
www.merriam-webster.com
Let's be frank: it isn't really empathy that's the problem. It's the political ideology behind the current revision of empathy that is the problem, and the culprit is usually some form of anti-Christian antipathy that seeks to undermine the presence of the Christian faith in society at large.
We all know this. So, as it stands, we who are Christian need to not only learn to better empathize with other people who are suffering, but sympathize and even transcend mere empathy and sympathy by expressing genuine compassion------like Jesus did.
Somehow, though, where politics comes into play, many who identify themselves as Christian excuse themselves from compassion by attacking a 'toxic empathy.' Maybe they need to lay out more precisely what non-toxic empathy is? Then again, maybe they need to acknowledge the need for showing compassion and lay out what they think that is?