You can catch an infiltrator in the midst of committing a crime. Such as changing signs, stealing gold from the tax office or assaulting a noble for example. You cannot order your unit to arrest an infiltrator who happens to be passing through your lands and not committing any crimes. Further, lets say that there are only two nobles in a region. Realm A and Realm B. The noble from realm B assaults the noble from realm A and does not get caught, but successfully assaults the noble. Now, you can infer that the noble from realm B is an infiltrator and you can infer that they are the one that is guilty of the assault. However you cannot send a police unit to the region and push a button to arrest the Infiltrator.
If a priest tries to do something that provokes the commoners of a region such as, Auto Da Fe or declaring yourself Lord of a region and a few other commands like that, then the priest has a chance of being arrested just like an Infiltrator who assaults, steals, etc...
A priest preaching is the lowliest action that a priest can take. They could be making the peasants hate you or lower their morale or building a shrine. Preaching isn't something that you should worry about. It is what happens later, after the preaching that you need to worry about.
Still doesn't change the fact that the mechanics as they stand
reduce rather than
increase the possibility of war.
They incentivize going and preaching anywhere (as you said, a mild provocation), but disincentivize arresting the priest (the escalation). More free arresting would disincentivize preaching in unfriendly places (so less mild provocations), but incentivize arresting (the escalation). I tend to think the second is more likely to create wars.
