What is a word for situation on people ignoring unimportant people?
Precisely in the situation that people are trying to ignore people in a polite way
English Language Learners Stack Exchange is a question and answer site for speakers of other languages learning English. It only takes a minute to sign up.Sign up to join this community
people ignoring unimportant people ... in a polite way
You're kind of looking for an antonym of "snub", which still includes being ignored...which will almost by definition be hard to be interpreted as polite.
The closest thing I can think of is the expression "smile and nod", which is the idea that you don't really respond to someone and you're just letting them say what they feel like saying. The reason it can be interpreted as polite is that a reaction was given--but not one that took the conversation further.
The likely-unusual-to-new-speakers word "nod" means to raise and lower your head in a way to suggest "yes" or "agreement". Though in here it implies this is just a polite way of not getting into a confrontation with someone--vs. actually agreeing or being interested in their issue.
The expression cold shoulder might be appropriate, though it's not specifically about somebody that is unimportant. it might also be used in other circumstances, for example guests who have overstayed their welcome.
He gave them the cold shoulder.
According to the Cambridge Dictionary, it can also be used as a verb:
He was cold-shouldered by all of his colleagues.
If a person were simply in the state of being ignored, then you may refer to them as being "beneath notice". Examples of this occur in movies where the staff of wealthy individuals commit crimes but are overlooked initially as potential suspects, e.g. "the butler did it."
Fundamentally I believe it depends on the situation. A news reporter who is ignoring the people who are trying to be seen on air can be said to be "trying to stay focused on his/her task"