If the term fascism is to have any meaning, it must refer to regimes that exhibit the following characteristics: 1) exaltation of a particular people or Volk above all others; 2) a single maximum leader; 3) only one political party is allowed; 4) there is no freedom of speech and information; the media are strictly controlled; 5) through propaganda and coercion, the population is regimented.
None of these conditions occur in the Islamic world today. Muslims are not of one ethnicity, or even one race. Since the demise of the caliphate in 1922, there has been no one who could claim to be the maximum leader. And so forth.
We are sometimes told that fundamentalist Christians aspire to create a fascist regime. This latency hypothesis is another dodge, though, because how many of the conditions could they ever hope to establish, even in a worst case scenario?
Today there is one nation that meets all the criteria for fascism: North Korea. Yet that repressive regime is never (as far as I am aware) called fascist. It seems that leftwing regimes are a protected species in this sense.
The moral is that if you want to establish a rightwing fascist regime, go ahead. Just be sure that you use the hammer and sickle on your flag and make a token obeisance to the writings of Karl Marx.