In my opinion, you should only go to your manager if it has an effect on your work. Even then it's rare. Since you're the new guy and the others have presumably been there for a while... You will find it difficult to make your case. You risk running up against the trope of not being a 'team player'.

Honestly what you described does not sound that bad. You should think about other similar situations in your past that you have had with other people and try to see if you have a pattern of needing to be right. It is entirely possible you are externalizing some fault in your own personality.

Regardless, look at it as a learning opportunity. If you can't handle the various personalities in the world without it effecting you on a personal level, you're going to have a tough time.