The demonym I've most commonly seen is Clojurian.

Clojurist makes it sound like adherents to a belief, which does imply identity though Clojurian more directly so. I’ve also found Clojurian most often. If only we had software that indexed the popularity of words…

In that case, Clojurians can be used for new initiates and Clojurists can be used for the most dogmatic Clojure supremacists, like myself.