Is there any English "folk wisdom" proverb about how one should not meddle in an ongoing argument between a married couple?
keep one's nose out of something, according to Cambridge Dictionary:
to not become involved in other people's activities or relationships
This isn't applicable specifically to a couple's dispute, but "Why do you look at the mote in your neighbor's eye, and pay no attention to the plank in your own," or some variation on the idiom, has a similar meaning. Generally, don't worry about other's problems, especially when you have problems of your own.