You have the grounds for it in Albania, the last tribal society in Europe (discounting Scottish football). Then again Islamist Republics have a tendency to arise, much like Bolshevism, in the place wouldn't assume. I doubt Afghanistan would have gone the Taliban route without Soviet intervention both as a catalyst for militancy and setting up the bureaucratic framework. Iran is the perfect analogue to Communism in un-industruial states in that it was without a doubt the most western, secular Muslim country on earth, including Pakistan, indeed ironically it still is very secular, with Islam more a political than theological force there. Even Libya, its Islamism is/was mixed in with Arab Socialist doctrine, in an urban coastal society, used to Westen culture and then forced on the interior.
Any POD you're looking to?
Without major timeline change, I cant see a chance for an Islamist Albania before 1990 onwards and then without the USSR, the Yugoslav wars would be a precedent for NATO/UN/EU to stamp down on such extremists.
Actually depending on what you want, Hoxha might be your man. He was a stern Marxist but frankly if his power was threatened I can see him pulling a Saddam and pulling faith into his secular dictatorship for strength. Say post-Tito, Yugoslavia decides to pressure Albania by now abandoned by both the USSR and non-Maoist China, in attempt to flex muscle, unite the nation against a frankly evil enemy (mellowed parallels between Doi Moi Vietnam and Khmer Rouge Cambodia are welcome).
No invasion because the Warsaw Pact would step simply to retain a balance of power before the Yanks did, simply Belgrade sabre-rattling for some short-term "look over there" problem hiding propaganda.
However, after envoking Islam for his benefit, there's no way Hoxha or more accurately Albania could ignore it, particularly as its been raised in a nationalist tone. Horrible images of a far worse Kosovo are flashing in my mind. Post-USSR, and post-Hoxha, I can see an Istan style corrupt pseudo-Soviet dictatorship rising, however relying on Islam as a way to keep Albanians isolated and feel threatened by the Christian west. Let this build, come Milosevic and Kosovo this could boil over into an Islamic Albanian Republic being formed, no doubt for pragmatic reasons, but it wouldn't take long for a shrewd cleric to push things further or take total control. Picture grandiose plans of uniting the Balkans Muslim population and you have a Balkan War and Genocide in one.