In short I dont believe a Christian can be a Christianist and I dont believe a Muslim can be a Islamist.
I would say one can be a Christian or Muslim for example.
I have no idea whether a Christian can be a Christianist or not, because I am unfamiliar with the term.
As for whether Muslims can be Islamists, the fact is that there are Islamists, such as Muslim Brotherhood, Hamas, Ayotollahs of Iran, Boko Haram, ISIS, El Qaeda, etc. etc.
It is well defined by the actions and attitudes of these people, who call themselves Muslims.Discussing whether they are Muslims or not is like discussing whether or not Obama is a Christian or Pelosi is a Catholic.
But as long as Boko Haram exists, and draws upon Islamic holy texts and holy traditions, and as long as Boko Haram is fundamentally different that other forms of Islam, then distinguishing Islamism from Islam is a useful exercise.
The definition itself is well enough known, and well enough established that real communication is possible by using this term.
danielpipes.org/954/distinguishing-between-islam-and-islamism
If people want to use some other term to distinguish Islamism from Islam, that is fine too. Understand though, that there are terms that accurately describe the phemenon that are not allowed in CAF.