In the case of animated objects, is there any reason a Harbinger wouldn't be able to use Dark Claim? Party members are trying to claim that since animated objects are not sentient I cannot claim them.
So far as I can tell, there's no mention of a harbinger being unable to use on a nonsentient or nonsapient creature the supernatural ability dark claim.1 To rephrase this positively: So far as I can tell, a harbinger can use the supernatural ability dark claim on any opponent
For example, the ability maneuvers readied, in part, says
[F]or the harbinger to recover maneuvers, she must tap into her sorcerous malice by activating her dark claim class feature; the harbinger recovers a single expended maneuver whenever she Claims a creature, and she recovers a number of expended maneuvers equal to her harbinger initiation modifier (minimum 2) whenever a creature she has Claimed is reduced to 0 or less hit points. (Path of War Expanded 8)
And the ability dark claim says
[A] harbinger gains the ability to reach out with her sorcerous malice, marking foes as her own. As a swift action, the harbinger may Claim an opponent that she can see…. A harbinger can have a maximum number of creatures Claimed equal to her harbinger initiation modifier (minimum 1), and may not Claim a creature she has already Claimed until or unless the Claim expires.… [T]he harbinger automatically knows the position of creatures she has Claimed.… (ibid.)
(Nonstandard capitalization as per the original.) Thus there's no mention in these basic abilities of the harbinger needing to Claim a sapient creature to receive these abilities' benefits. In fact, according to the descriptive text, the harbinger brings to bear her own "sorcerous malice" upon her opponent, and what kind of opponent is irrelevant.
To be thorough, later harbinger class features that are tied to the harbinger having a Claim on an opponent also don't mention any limitations on the kind of opponent:
- The supernatural ability bleak prophecy at level 12 causes those creatures that the harbinger Claims to gain the condition shaken. While the typical animated object, for instance, is immune to that condition, so are many creatures, including any typical level 3 or higher paladin, making this hollow evidence of sapience being necessary for a harbinger to Claim a creature.
- The supernatural ability dark murmur at level 13 sees the harbinger no longer provoke attacks of opportunity for her movement from creatures that she Claims. Why? The description says, "Those claimed by the harbinger find her as hard to catch as rumor itself" (9), which to this reader sounds like code for Because it's cool rather than, for instance, Because the creature that the harbinger Claimed views the harbinger as the specter of death, it hesitates to strike the harbinger lest the harbinger retaliate and slay it (perhaps implying that a creature without an Intelligence score might be immune to the Claim as the creature may not even understand what death is)… or, y'know, whatever.
None of Path's feats that have as one of their prerequisites The ability to claim creatures or the dark claim ability specify that a creature that the harbinger Claims must be sapient. No maneuvers even mention that a harbinger must Claim a target creature, much less that the creature be sapient. To be extra thorough, I searched Path for the word intelligence, and while it appears several times, the word intelligence does not appear in a context that limits the creatures a harbinger can use the dark claim ability against. It's difficult to prove a negative—and, to be clear, I've not strayed beyond Path of War Expanded—, but I find no evidence of the other players' claims. Likewise,—to be super thorough—the term mindless appears only in the context of the supernatural ability hearten the mindless that can be gained from the conviction class feature of the zealot.
With all this in mind, I really don't know where the other players got the idea that a harbinger can't claim a nonsapient creature. The other two Path of War classes have a particular alternative way of recovering expended maneuvers—the mystic by surging, the zealot by aiding another—, and the dark claim ability is the harbinger's. Denying the harbinger this mechanic weakens a harbinger for—so far as I can tell—no good reason.
I suggest that if the other players remain unconvinced that you have them try to view the dark claim ability not as an external effect but an internal one that's unique to the harbinger. The harbinger does not, for example, bestow upon the opponent the condition Claimed (which isn't a thing anyway), but, instead, the harbinger Claims a creature—not You have been Claimed! but I Claim you!—, and it's that act of "sorcerous malice" on the part of the harbinger that empowers her and that—at level 12 and higher—scares the crap out of those opponents… if they aren't, like, animated objects or level 3 or higher paladins or other creatures that are immune to fear, of course.
1 Path refers repeatedly in its descriptive text to sapient creatures but doesn't mention sentient creatures. Further, by my reading, Path associates no mechanics with being sapient. In context, it seems to employ sapient to mean possessing an Intelligence score of at least 3, the minimum Intelligence score in Pathfinder for the possession a language and, for instance, to avoid being handled or pushed by the skill Handle Animal. However, the Pathfinder rules don't seem to use the term sapient at all, using instead sentient and using that word to mean possessing an Intelligence score, like most creatures from a lizard to a solar do as opposed to possessing Intelligence as a nonability like the typical animated object, giant spider, or skeleton does. In other words, if the other players are objecting based on sapience or sapient then their objections lack a mechanical foundation, and if they're objecting based on sentience or sentient then Path doesn't even use those terms.
Assuming you are fighting said object, yes you can Claim non-sapients*
Dark Claim has "specific" (really, non-specific) targeting requirements; you must consider them an enemy.
As a swift action, the harbinger may Claim an opponent that she can see...
Other portions of the ability refer to Creatures, which is a game-term in Pathfinder
A harbinger can have a maximum number of creatures Claimed... may not Claim a creature she has already Claimed... (etc)
*It usually goes without saying, but the GM (not other party members) has the right and responsibility to interpret the rules in a way that they deem fun and fair. Usually, this means they will agree that Dark Claim works fine on all creatures including Constructs.
However, a small number of GMs may adjudicate (for the same reasons the other player had, as an example) that there must be something to Claim that non-sapients don't have (e.g. an identity or soul). If you have concerns about this type of ruling, I strongly recommend talking to your GM in an open way outside of game time.