You have to start with things you agree with. Don't get hung up on specific details, if you have to misinterpret them in order to agree with them then start there. Then once you establish agreement, find out why they believe what they believe in an issue, and repeat back to them what you think you understand (very important, and its okay to guess if not sure). Then connect it to why you agree, how those things are connected, and how this connects to what they value, bonus points if you can add class analysis.

Granted, the minute you walk away they could just put on fox news and undo it all. If your family member is merely backward, then you can help them catch up. It's a long term strategy, there's no shortcut, and you might never turn them into a full fledged lefty, or it might take a long time.

Look up nonviolent communication strategies to drill down on some of the fundamentals. And don't forget to connect over shared interests! Music and books and shows are easier to find points of agreement, since they are engineered to have broad mass appeal, than political points which are engineered to sow division. Only a real social connection can dechuddify someone.