I used to think that "false empathy" meant when you are basically empathizing with someone, sympathizing, or sort of getting into their emotional drama etc....
Now I see it is more than that. It means really `joining` with someone in, and agreeing about, ANY kind of ego scenario, relating to ANY appearance or ANY illusion that covers up the immortal, God-created Real Self.
If a person comes along and is in any way demonstrating belief in being anything less than God created them, perfectly whole and holy and innocent and invulnerable, then that's an ego drama. If I go along with it, buy into it, join with them in it, participate in it, take it seriously, listen to it, judge it, engage with it or any of that, that's me entering into false empathy.
It's kind of like a false Oneness... a false joining, that says, I will join with you in a subjective illusion and pretend it is objectively real, and the two of us will then be 'infected' with this ego attitude and at least we'll agree with each other that this it the truth.
Real empathy then would entail absolutely not joining in ANY ego whatsoever, overlooking all ego, persona, and appearances, not believing in or taking seriously ANY presentation that runs against that (including anyone seeming to be sick, diseased, afraid, upset, etc)... holding the light, holding the truth, being a beacon, a leader, and strength that invites the other person to remember who they really are.