Is it necessary to be a Hindu or believe in Hindu deities for Yantras to work?
Not at all. Yantras are symbolic manifestations of universal and divine energy systems, which India happened to be the first to discover and, perhaps inevitably, interpreted through the prism of local cultural sensibilities. The Lines of Force that constitute the body of the Yantra are universal in their power, relevance and application. The healing energy may be called Hermes or Dhanwantari or Reiki but it is the same energy all over the world. The pure and protective feminine power may be called Athena or Durga or the Kwan Kin, but it is again the same power. The Yantra works as a synergistic and transcendental system; the Hindu nomenclature that is used to describe its parts is incidental.
