Try this:
Being empathetic as a default disposition. As a way of living, as a way of navigating the world.
Don't reserve empathy for certain people in certain situations when you're in certain moods.
And remember that empathy doesn't mean condoning behaviors that don't deserve condoning. Empathy doesn't mean being nice to people who have done hurtful things.
Always leading with empathy allows us to make the important distinctions around when and how to respond to emerging situations and evolving contexts and unpredictable human behaviors.
Empathy is non-judgmental, which is not the same as making a decision on whether to support someone's actions or behaviors or words.
Empathy requires curiosity, equanimity, reflection, and vulnerability.
Vulnerability is the key thing. I suspect that people who are not empathetic are too afraid to be vulnerable. They aren't comfortable staying present and/or they conflate being empathetic with commitment, and/or they are unwilling to validate the lived experiences of people not like them.
Empathy isn't soft or weak or irrelevant. Conversely, being empathetic is one of the most courageous and empowering and impactful things we can do.
Especially for people with privilege and power and authority.
Try it out. And see how it goes.