You can be loyal to both countries - you just have to refrain from doing things that betray your loyalty to one of these countries. There are many Israeli-Aussies, and they NEVER would abuse their Aussie citizenship or passports for the sake of Mossad. If you want to enroll in Mossad or Shin Bet or any agency which may create trouble for Australia, you should renonce your Aussie citizenship first.
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Former IDF general Avigdor 'Yanush' Ben-Gal dies at 80 (Haaretz)
from the article: Torn between two passports: Prisoner X and dual citizenship