I think it's often useful to get people to change their minds on moral or politically-charged issues, particularly in EA, where we would like certain people to allocate their time or money differently. For many people, changing their mind requires an emotional and rhetorical component that has to be executed carefully. Anecdotally, I've noticed that many of my EA friends are not very good at this.
This post has the best description I've seen for getting people to change their minds-- it's talking largely about certain issues that were particularly relevant around the 2016 elections, but I think it works for any moral circle expansion.
Relevant segment pasted below, though the post has lots of helpful examples:
"3. Figure out what values you might share with the potential ally.
4. Make a gentle statement about how your shared values shape your understanding of the topic at hand.
5. If they become defensive or angry or argumentative, de-escalate the situation and change the topic while making it clear you still hold to your values.
6. If they respond with curiosity or confusion or even apathy, keep going.
7. Find a way to express compassion and understanding for how the potential ally ended up with the opinions they have now (tip: develop compassion and love for your past self, who was almost certainly more racist, homophobic, etc. than you are now).
8. Make yourself vulnerable in some way: share a time you made a mistake, or something you feel ashamed of, or a time you were hurt.
9. Share a personal story about the topic: something that changed your mind, or an “aha!” moment when suddenly you understood why something was wrong (but be sure to preserve the privacy of others when appropriate).
10. Help them have compassion for the targets of oppression: talk about how the target must feel, make an analogy with a group the potential ally has an easier time empathizing with, share your own feelings of compassion and love for the targets.
11. Restate your values and how they inform your opinion on this topic, warmly and clearly.
12. If they have another comment or question, repeat from “Find a way to express compassion” until they run out of questions, or you run out of energy.
13. End by changing the subject to something you both enjoy, or expressing your feelings of warmth and connection for the potential ally."
I might add that I find that if you always try and change people's minds they learn that you don't care for who they are. I would recommend being people's friends and then taking time when relevant to try and change minds. (If you want to change everyone's mind I doubt doing it 1 by 1 is particuarly effective anyway)
This seems right!