Being friends with two people that dislike each other due to similar personalities

Has anyone had the awkward experience of being friends with two people that disliked each other? I know there has been plenty of cases where there was a good reason for it, usually because one of the two friends really wasn't very nice or a toxic friend. But there has been a couple cases where I honestly believe they are both good friends, they just dislike each other due to very similar personalities, both positive and negative. Although most cases involved them both hating each other's negative traits since they were identical. And in some cases, even hated the positives in the other, stating it was a forced act.

In some cases this can create a wonderful long lasting friendship, other times it can create disdain towards one another. When it's two of them having a disliking towards one another, I believe it's because they have a lot of negative traits that are practically the same between the two and they hate seeing their own negative traits in the other person. Like I knew two friends that disliked each other because they hated being wrong and didn't like taking responsibility for their own actions. I know one friend that still talks about the other person they used to be friends with and vise versa.

They both liked being in the center of attention to an extent and hated each other for it. Also I've seen it where both friends may have been a bit flaky so they would complain about each other's flakiness. Both of them were right about each other. If you encountered this scenario, did you put distance between yourselves and quietly pick sides or stay neutral? Did you ever try saying anything to both of them, trying to say that the things they are complaining about are the exact same things they do themselves?

Another thing I've seen is two people stating that they are clingy. And the truth was, they were both clingy, had boundary issues. So technically, they were right about each other and this caused friction between them. If it is due to them being arrogant and not wanting to be wrong or persistently flaky, I usually distance myself from both of them. But if it is something that is minor and they are just hating each other for it, I will secretly stay neutral since they are both right about each other. In any cases like this, has one or both of them secretly try to get you to stop hanging out with the other? For me, I don't pick sides unless there's a very good reason to do so. Just wondered what you guys thought.