All of the DW PC professions must have some form of deadly active fighting ability. The DW version of a cleric/priest is a character without any magical or combat training/skill that would usually - when faced with an armed & deadly adversary - get chopped up into tiny bits unless a trained Knight/Sorceror/etc. intervenes. Clerics/priests are therefore usually only found as NPCs.
However... personally I don't see why a PC can't be some form of holy or saintly warrior (e.g. 'Paladin'=Knight or 'Martial-artist Priest'=Mystic, etc.). The True Faith has it's own views on overt magic, which might be a problem - as Jason mentioned - but the Mystic profession itself does not appear to be connected with any specific religion. Therefore, as Kintire inferred, the 'power of the mind' could easily be misinterpreted as 'divine intervention'.
The great thing about DW is that it gives you some breathing space to permit ninja priests as PCs or not, whichever you prefer! That being said, who knows what new DW professions might appear in the future...?