This is fantastic! So in the past I've tried "Islamist" as a term to describe conservative forms of Islam. I'm not at all attached to a particular term, but it would be great for the world if we could agree to a term for "that subset of Muslims that hold those more conservative beliefs". Any ideas? Would you be okay with "Islamist" ?
How about 'conservative forms of Islam' or perhaps 'Islamic conservatism'? 'Islamism' as a term has already been taken to refer to one particular brand - or rather set of brands - of Islam. And indeed many such forms of Islam are pretty recent phenomena or even a kind of reformation within Islam (although not, I would say, the kind that should be encouraged!). Many of my more conservative fellow Muslims don't buy into this brand of Islam at all. They may be more morally conservative (as individuals), but they aren't sympathetic to the kinds of political or militant movements that are typically labelled as 'Islamist'. But always keep in mind that there are many degrees of Islamic conservatism too.