It might be helpful if I add some context to my post.
I live on several acres surrounded by forest. The incident described happened as we were sitting on the tailgate of my truck at the open door of my rather large post frame outbuilding. My friend had come to visit unannounced and not
expected. That’s okay, it’s common for us to do so. He had been here for twenty or so minutes before asking the question.

I was not in a frame of mind to be discussing what has been a politically charged subject so I deflected in an attempt to steer the conversation in a more cheerful direction. To my mind this was prudent.

Keep in mind he entered my property and approached me, not the other way around. It was just the two of us present.

I was not troubled that he immediately left, that was his choice. What surprised me was the anger he exhibited. He has not contacted me since and I am, well, perplexed.

"Stormed off in anger" ?????? ummmmm, or fear they were being exposed to a germ-carrying pratt...that would be You.
If you were actually a friend, you would be happy to allay their fears.

Obviously you are more protective of your rights than your friends right to be sure of their safety regarding the virus.

You seem like a rational person therefore I am very perplexed as to why you were perplexed.

Your neighbor had a right to know if you were not vaccinated and possibly asymptomatic. You could have passed it on to him unsuspectingy. He was within his right to ask and be informed, as was his right to walk away. IMO you were in the wrong.

Your friend was trying to determine the safety of sitting near you in a closed space(?). If you had been vaxed then you would probably have just answered. Being evasive (private) suggested you had not. This is my guess as I was not there so have only your side of the story to go by.