[one problem with having priests Arnak everywhere is that RM magic is crawling with investigation spells which do not require RRs, especially in Mentalism and Channeling - and PCs are notoriously suspicious. And my take is that priests Arnak know that they are vulnerable to investigation magic, so they most often act through proxies. There are ways to hide from investigation spells, but they are used only when proxies are not convenient, which is not that often]
I played a Mentalist in a Shadow World campaign years ago. Using the Presence List wasn't too helpful as Feel typing spells all allow Resistance Rolls. Our group Channeler had better luck with Detect Evil from the Lore List but still allows a RR.
All "P" type spells only allow RRs (and they only allow it at GM's discretion) to determine if the target is aware of the spell. It does NOT prevent the spell from working as indented. Worst case for the PC, the Priest Arnak is aware that a detection spell has been cast on them, but does not know what spell, and might not even know who the caster was (the "Feel" spells indicate that "the target must first be located by Presence of Presence True", indicating that LOS is apparently not required for the spell).
As almost all detection spells are P spells, almost all of them cannot be resisted naturally. The only regular way to foil them is to misdirect, but not all classes have access to misdirection spells and they happen to be of limited duration. Furthermore, having spells active at all times also draws attention because it triggers other detection spells.
Priests Arnak who are public figures (some of them are) *must* have that kind of protection, because their everyday role requires it. The others ? Not so much, and I would assume that (since the Priests Arnak come from various professions) that they tend to select their "public faces" from those who have suitable professions, but most of them do not need it on a daily basis - their most potent defense is to avoid attracting attention - there is nothing worse than being on the receiving end of a well-timed Mind Typing spell, and being Mind Stored is just one step away from being GPS tracked.
If the PCs are incrediabily powerful (or lucky with open-ended rolls) :
1) Misfeel spells can counter ( in Magent and Mystic lists)
2) other powerful individuals in the vicinity may take offense to "random probing"
3) even if the PCs get a positive ID from a spell, it is their word against the accused priest. These guys usually have a lot of political clout...so if a PC points a finger at a well respected "pillar of the community", who will the town guard throw in jail?
Why would they do that ? If the PCs are really willing to cross a Priest Arnak, they will certainly not try to move against them politically unless they have more powerful allies, but PCs can be driven to radical solutions and mystic-like powers can work both ways - "accidents" may happen, and Priests Arnak in a social environment cannot bring the full strength of the Orders to protect themselves physically (those Messengers are not really subtle), so a well-timed ambush or assassination helped by a few misdirection spells can both get rid of the Priest and obfuscate investigation.
And as far as I'm concerned, the Priests Arnak *know* they are vulnerable to determined people. Their best defence is to avoid being in the same place as those pesky troubleshooters and work indirectly whenever possible. I would go so far as to assume that they only work directly when they need to use their power (for subversion or corruption, for instance - there are a number of examples given in the books) and cannot trust proxies to do it.
But otherwise ? They are, as Terry put it, about 30-40 Priests for a whole continent. Micro-managing every little plot will get them nowhere, especially since there is a something as a chain of command and some of them must have support or coordination roles. Add to that the fact that they also must conduct investigation on rival parties and work to consolidate the footholds they have, and they have to intervene personally on a long-term basis when trying to corrupt a specific target... and that pretending to fulfill a public role consumes a large amount of time, and they simply don't have the time to worry about adventurers personally. After all, if they retreat to the shadows for a decade or two, the impact on their long-term plan is negligible, so why take the chance ?