Offer Examples of Changing Minds
Remind your friend or relative about a time that they changed their mind or that you changed your mind - not even about something social justice-y necessarily, just in general. This can be a great way to get out of a “stuck” moment where they might want to end the conversation with “I guess we’ll just never see eye-to-eye.” Have an idea in mind in advance of the example you want to give, so you’ll be ready to respond, “It seems that way. Remember when you thought you’d never like Jane’s girlfriend though? And now you love her. And I used to say I wasn’t a feminist. But I changed my mind. So I do think that changing minds is possible, and that might happen here someday, too.”
The result of this is putting a little crack in your person’s resolve that their worldview is static, which can open them up to eventually integrating new ideas into that worldview.