'fake deep' is a description equivalent to an overt chauvinistic person. They appear 'smart,' 'educated,' or 'woke' upon first impression but the underlying meanings of their words contradict intent.

Intelligence agency term for "psychological operation". A government or corporate-sponsored operation, usually taking the form of a "terrorist attack" or "crazed gunman on a spree", with the intent of panicking the public into demanding more police and laws inhibiting freedom. Psyops are usually carried out by drugging a civilian or group of civilians with aggression-promoting drugs, psyching them up, arming them, and sending them out to commit mayhem. Government-sponsored terrorism. See also blackshirts, conspiracy

It is the act of trying to appear "woke" or "depressed" on a social media site to gain followers. It is usually built around a fake persona, built with the need to 'fit in' when in reality, it undermines real mental disorders, and could sometimes lead to legitimate depression. If you're suffering from depression, call your local hotline.