Nope. You've lost me there.

It’s neither right-wing nor left-wing.

They're conservative religious views. Of course it's right wing. Same as conservative Christians in the US or Uganda, or the Hindu nationalism we see in India.

This sort of claim always strikes me as fairly cheap politics by people on the left.

I disagree. It's just calling a spade a spade.

From the Wikipedia summary on far-right politics, which I found to be a fair description:

"Far-right politics, or right-wing extremism, is a spectrum of political thought that tends to be radically conservative, ultra-nationalist, and authoritarian, often also including nativist tendencies."

"Contemporary definitions now include neo-fascism, neo-Nazism, the Third Position, the alt-right, racial supremacism and other ideologies or organizations that feature aspects of authoritarian, ultra-nationalist, chauvinist, xenophobic, theocratic, racist, homophobic, transphobic, or reactionary views."

"Far-right politics have led to oppression, political violence, forced assimilation, ethnic cleansing, and genocide against groups of people based on their supposed inferiority or their perceived threat to the native ethnic group, nation, state, national religion, dominant culture, or conservative social institutions."

Seems to me that islamism lines up with that very well.

'When people do bad things it’s right-wing, when they do good things it’s left-wing.’ etc

Respectfully, that's not true.

You find very, very few people who call Stalin, Mao, Pol Pot, etc right wing. Far less than you see far-right people trundle out the tired "Nazis were left wing because National Socialists" nonsense.