I'd say that a 2x PP multiplier of Loki would ping to a priest of Thor, it's a "Holy object" of an oppositional diety. . .at bare minimum an actively cast channeling spell would react. I'd likely have it ping inactive on a table. . .it would respond to a "Black lore" (Or "white lore" from a priest of loki). . .I think the inability to normally avoid that kind of detect is one of the signifigant drawbacks of being a channeler.
In terms of the holy shout spell, priests will often dump it into the middle of a melee, it's like a stun grenade that only effects enemies. . . .if it's a popular enough spell for a militant priest PC, it's going to be hard to plant an agent who's the channeler of an opposed god into the party.
The "inspirations" angle came up via Power Perception. . . .the mage who always stood back and observed with it, waiting to snuff the first enemy caster or item wielder who entered combat noticed that the rogue never took on the halo the other PCs did when the Paladin started in with his war cry (cast inspirations).
Let me put it this way. . . there are holy items that can only be properly used by a channeler of a given diety. . . .and they'll just not work right for anyone, and likely will harm a worshipper of an opposed god who picks it up, or zap a channeler of an opposed god who picks it up. . .there are some items in CT that directly damage "wrong" weilders rather than going the Will contest route. . .being a channeler imbues you with a specific variant status.
As to the "It's too easy to find them" what's good for the goose is good for the gander. . .unless the GM house rule tones down detect and lore spells, a suspicious mid level caster will bust you fairly easily. . .so the PCs can use that, but then so can NPCs use it on them. . .
Essentially every religion I can think of has a "Martyrdom" concept. . .that being singled out for your faith and persecuted or killed for that reason alone is a risk you take, and a trial that leads to a reward for sticking to your faith in the face of convienience or safety. . .
You wave the flag, you take the PPs, you pray those spells, you are an "elect" among worshippers, you stand out from the flock, and if anything it's your duty to be the one who the hammer falls on. . .you're a budding martyr for the cause, just like countless heroes, saints and holy people in our world refused to hide what they were and died for it.
Easy enough to have misfeel magic items for those instances when the plot needs these kinds of effects not to work. . .or if you want your world to be more mysterious, you can chop down the lores/detects. (If I recall, the Ravenloft setting essentially eliminated detect/divination spells from use for flavor purposes.)
