"Not your onions!" is the kind of phrase that sounds ludicrous until you grasp how frequently people step into things not theirs to carry. It's a clear, almost humorous reminder to mind your own affairs and to release weights that are not yours. Like going into a kitchen and stirring a pot that was never yours—you might get burned or worse, damage something that was okay before you touched it.
There is something liberating about acknowledging what is not yours. Not every conflict calls your presence, not every story needs your voice, and not every issue demands your opinion. Sometimes wisdom is just retreating and declaring, "those are not my onions."
It does not follow that you are indifferent. It means you get boundaries. You know when to let others deal with their own mess, their own growth, their own repercussions; you also know when to help. Life becomes simpler when you quit peeling layers never yours to begin with, when you stop carrying everyone else's burden.
Thus, when events begin to draw you in drama, fights, unwarranted tension, just stop and remember: not your onions.