Empathy is the best tool

[Alan V]

This sounds like a good idea to me. But in practice, I'm afraid, it appears to be extremely difficult to stick to. 

We all think empathy is great. Then we all see that it's about the easiest thing in the world to switch off. Once it is discovered that someone falls outside the range of the locally acceptable ideology, then that person will almost certainly stop receiving empathy. 

For example, if you were to start a thread on this forum expressing the opinion that Donald Trump is good for the country, or that trans women aren't really women, you would not find that people respond by making you feel understood. No one will say, "I get where you're coming from, but [sympathetically expressed attempt to persuade]." 

I suspect people will argue that such opinions are so far out of the realm of acceptability that no empathy should be given to the person who holds them. Which means that empathy fails to cover a very wide range of disagreement.

Are you saying that we should be empathetic with those who are not empathetic? That we should be tolerant of the intolerant?

I don't believe you have thought this through. Those are not the ways to promote empathy and tolerance IMO.