What is the perfect idiom for someone doesn't or act like you aren't there? For instance, a group of two people are chatting and you are trying to join in with the conversation but they continue to chat with each other.
These idioms refer to the behavior, as opposed to the person engaging in that behavior. I'm not aware of an English idiom meaning "someone who gives one the cold shoulder". Related, but not an exact match, would be the word "snob", which applies to someone who feels superiority over others, and displays that feeling through stand-offish behavior.
To cut someone dead, according to Macmillan Dictionary:
to pretend not to see or recognize someone that you know, or to refuse to talk to them
Attribution: Definition and synonyms of cut someone dead from the online English dictionary from Macmillan Publishers Limited.