Personality is not relevant when determining if someone is correct or not, but it does empirically matter in terms of how likely someone is to get something done based on that. If you think being right is the only thing that should matter, you've achieved your goal already once you reach that step, so congrats! If you agree that it's not the success criteria, it makes sense to start paying attention to those other factors, or else you'll end up only being right and not successful.

I'd argue that if these issues are important to you, and you want to convince people, you'll be more effective if you find a more compelling argument than "you aren't allowed to care about what you just told me you care about".