Who would want to decorate their church with statues that are indistinguishable from actual monsters?! They would be a pretty good deterrent against intruders since they would expect the statues to attack at any moment, though.
You know that the D&D gargoyle is based on the real-world church statues, and not the other way around, right?
In my game, the default assumption is that most people are not aware that gargoyles are actual creatures, they are just a common statue that decorate certain types of architecture - maybe for a mystical reason, maybe for tradition. (Maybe to act as camouflage for the real gargoyles they use as guardians.)
The default assumption in your game may be different. And of course, adventurer's are not "most people", but I don't assume they have special knowledge of uncommon monsters until they are higher level, or are playing a character that has a reason to know such things off-hand (monster hunter, wizard who studies rare monsters for use in alchemy or taxidermy, etc.)
[Edit] Just want to add, the situation in which you encounter the gargoyle would of course make a big difference. If you are on church grounds (and are not currently expecting danger) and there are gargoyle statues on all the eves, you probably wouldn't suspect anything and could easily be surprised.
Encountering an (apparent) gargoyle statue (or a statue of any kind) in a dungeon complex, evil cultist temple, or other dangerous area would merit suspicion whether or not you know about gargoyles as monsters.
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