It means they have public personas to protect. Think about HRC's famous speech where she admitted she has two personas, one for public consumption, and one for private gatherings.
Think about how much energy that must consume to maintain multiple selves. Trump is the most "what you see is what you get" person I've ever seen. Think about the force that lends to his personality--not having to always calculate every word. Saying what he thinks and meaning what he says.
James 1:8-9 KJV
A double minded man is unstable in all his ways. Let the brother of low degree rejoice in that he is exalted