In such an occasion I would I assume that I had met my future self, assuming that they were the same gender, height, and color as me but somewhat older. As freaky as that would be the truly terrifying thing would be the fact is apparently however far in the future that version of myself is, apparently nothing between then and now changed for me. Such stagnation might not be bad if you don’t realize it’s going on. It’s not like one day you’ll realize “oh shit my house looks exactly the same as it did five years ago!” However I would be bummed to realize that nothing would change, especially considering how much my families living room alone has changed over the years and how often those changes occur; and each one is indicative of something larger going on.
If it was obvious that the new acquaintance was NOT a future version of myself, I’m not sure what I would think. Maybe they would be an alternate universe version of myself.