To have empathy for someone is really being able to really see this other person and understand why they might have acted or said what they did. While it might not be logical to you given your background, it might actually be logical considering this other person’s specific background.
It’s the ability to hold the space in your mind that even though you might vehemently disagree with them, you also understand what makes them behave how they do.
This is very different from sympathizing with them. Sympathy is different in that not only do you understand the other party’s rationale, but you also have experienced it yourself. It’s expressing sorrow as you know what they’ve gone through, or that you understand and grieve for that person.
You’re accepting that this person’s reality is similar to one that you know and understand, and with it comes a lens of tolerance. It’s more of a “I get what you’re going through and it’s okay to be feeling/acting like you do.”
So while it’s necessary to empathize with white supremacists in order to understand how to get them to change their beliefs (or at least mitigate harm they might do), we cannot sympathize nor tolerate their hateful rhetoric and actions that are violent towards others.