Cannibals build effigies near player's base. There are also many spots on map where effigies are permanently (that is, they respawn on the same spot if you break them).
I've destroyed several effigies recently, because I needed cloth and skulls.
Will this increase cannibal hostility/presence? I've kept a low profile so far...
While I'm not exactly sure, I don't think destroying effigies increase cannibal hostility.
From the Forest wiki page on Hostility:
There are a number of ways to make the cannibals angry.
Attacking groups of cannibals, or being attacked by a group and fleeing
Killing cannibals and letting one or more escape afterwards.
Killing cave cannibals and mutants (even if none "escape").
Notice that destroying effigies is not listed.
Furthermore, from the wiki, effigies seem to be an indicator of cannibal Presence, not Hostility:
Hostility is how the cannibals will react to the player upon encounter (such as attacking or simply watching or growling)...
Presence refers to how often the player runs into the cannibals, both "randomly" in the wild and at bases. Presence is both inherent and generated.
Erecting an effigy seems to be an indicator of Cannibal presence, and not an act of hostility towards the foreigner (in the same way that cannibals will see your effigies as an indicator of your presence and stay away).
Finally, I have yet to experience any negative effects from destroying cannibal effigies (though YMMV, since I haven't kept as low of a profile as you have).
