It's unfortunately very common for people to weaponize empathy -- to call for empathy in order to tell people seeking justice to be quieter. Due to this frequent occurrence, I think it is common for people to view practicing empathy as antithetical to achieving justice. In this essay, I argue that the act of truly practicing empathy is much different than what is prescribed by many people who call for empathy, and that truly practicing empathy dovetails with (rather than opposes) justice.
For people wondering about how to engage in difficult, high-stakes conversations about politics without losing their cool, deeply empathize with others, and maybe change someone's mind, I think this book, Nonviolent Communication, is a good place to start. This book explains an empathetic way of communicating (both speaking and listening) that make difficult conversations easier and more productive.