I agree with much that was previously posted, and I will add what I think was not already mentioned:
You keep going by not always arguing. This can be done 2 ways: flat out taking a break, or move the argument to something more along a conversation or discussion. No more point-counter-point dynamic, but friendlier conversation.
With random internet people, I find that a break to “get to know them” is helpful because you both become more humanized. They might learn that you are not what they thought, and you have more of an “in” with their brain, than other random people.
With friends, always be respectful, and always try to steer the debate away from a win-lose proposition, to more of an information or inquisitive discussion about your respective beliefs. They might be stimulated into learning more that way because they are not building a wall against what you say but trying to understand your expression of your own beliefs.