What could I do to put an end to this and to set everyone straight?

I'll state the obvious but don't participate. These discussions have nowhere to go but south and you will get roped into something ugly. Have the courage to call them out and keep you out of their drama.

Not long ago I had a coworker badmouth our boss because he and my boss don't get along. This coworker was trying to "recruit" me to his "side". I got a little nasty about it and told him we're not going to have this discussion. If it's something work-related, cool. If not, get stepping.