Blue boy is a nickname which is in reference to a character in Season 1, Episode 1 of the show Dragnet. It affectionately indicates someone as having a distaste for convention and law while. A "blue boy" is a male who is anti-establishment, while still respecting life and personal freedoms.
"Why is Luke always on drugs and ranting about the government?"
"Lol, blue boy over there thinks he can save the world with a hit of LSD and a prayer."
Blue boy syndrome is when someone is obsessed with the boy band BROCKHAMPTON. The name comes from the cover art for SATURATION, SATURATION II and SATURATION III as all the cover arts feature different men either wearing blue, or having blue body paint.
Kevin: Have you seen Adam's obsession with BROCKHAMPTON?
Casper: Yeah, he has hardcore blue boy syndrome.