Our manager was off that day, so I decided to interfere in a friendly
manner and propose that they take a break and discuss things later to
cool off.
I don’t think you did the wrong thing, but it’s never clear how to handle something like this since—with the boss away—anything could happen.
In my experience, when stuff like this happens when supervision is happening, some kind of small power-play or “testing” of co-workers happens.
Option 1: Walk away from the fracas and be vocal about you leaving.
I don’t know where you work or what your constraints are, but if I were in the middle of something like this I would basically stand up and say, “I can’t work like this…” and walk out of the office. Not for the rest of the ay or the full day, but just a short break. Like maybe a walk around the block or a bathroom break. Depending on how well you know your co-workers—and the history of this behavior goes—I might even say, “I can’t work like this. I need to grab some coffee (or food). Anyone want to come with me?”
The outcome of this is never clear, but the message needs to be clear: Your behavior is standing in the way of my ability to do work.
Option 2: Make note of the details to share with your boss when they come back to the office.
Also, when your boss comes back it might be worth it to tell them what happened. Again this is all based on internal politics and such, but you generally should not let something this disruptive go unnoticed.
Option 3: Ignore it but still make note of the incident for future conversations with your boss.
That said, at the end of the day you utterly want to put proverbial blinders (and maybe actual headphones) on and ignore it, that is an option to. But I would still make a note of the incident for future reference.
Like if you meet with your boss sometime in the future and they want you to work with one of the folks embroiled in this argument. You can say, “You know, I didn’t want to make a big deal about this when it happened. But the person you want me to work with really caused a scene a while back and I don’t feel comfortable working with them.”
Not Optional: Completely ignoring this ever happened.
At the end of the day, whatever you choose to do remember one thing: Forgetting something like this happened won’t help anyone out there. You ultimately work at a job and need to work in an environment you feel comfortable it. If you cannot work in such an environment, it affects your productivity and the productivity of others. Don’t ignore it.