There are several other ways to express the act of intruding or interfering in someone else's business or affairs. Instead of "poking one's face in," one could use the phrase "butting in," "meddling," "prying," or "nosing around." Additionally, the idiom "sticking one's nose where it doesn't belong" effectively conveys the same message. It is essential to recognize that such behaviors are generally unwelcomed and often considered rude. It is always best to respect other people's boundaries and privacy, refrain from interfering in their lives unless invited to do so, and practice good etiquette to maintain healthy relationships.