I’d say its time to disengage from the conversation.
Having the conversations and sticking to your points is good and all but they didn’t come to their opinions based on “facts and logic” so you’re not going to facts and logic them into a different opinion.
Possibly try to pay attention to when your friend has gotten to the point in the conversation that they’ve effectively shut down and wind down the conversation when it gets to that point. Talk about something else, everybody goes outside and touches grass, or just call it a day.