Instalker
Someone who follows strangers on Instagram and follows every story they publish.
"I'm one of your instalkers and love your recent story on places to eat in Vietnam."
instalk
The act of stumbling upon someone's Instagram who you do not know and intensely analyzing all of their photos all the while leaving no trace of likes or comments.
"The principal thought I was a good kid until she instalked me and realized I deal meth to handicapped veterans"