Is this sentence natural?
You shouldn't poke your nose into other people's affairs.

Question

Answer

Yes, but most people replace the word "affairs" with the word "business" in the U.S.A.

Answer

I would say that it's not neutral.  It's got the tone of admonishing or finger-wagging and is also rather casual because of the phrase "poke your nose."  So it's more casual than formal and more for intimate/personal conversation than business.