This question is objective because the game as it stands cannot be played without knowing the answer
Spells within Pathfinder, such as Detect Evil and See Alignment cannot work, and Paladin, Inquisitor, Oracle, and Cleric classes break if the answer cannot be known. These spells and classes are extremely important to the game, and thus, rules for the system have been put in the Core Rulebook.
This question asks about how the system works, for which there is a definitive answer in the Core Rulebook. It asks whether Alignment is based on Intent or pure Acts, which is most certainly defined within the PF system, and the accepted answer demonstrates several sources straight from the Core Rules which demonstrate an objective answer to a question that the Pathfinder Developers anticipated.
Assuming otherwise would say that Paladins are entirely homebrew despite having official rules, because the system upon which their are based, which is definitely established in the core rules, is somehow "inherently subjective."
To say that the answer cannot be known, or is inherently subjective, means Organized Play cannot exist.
Assuming that any answer to this question is inherrently subjective means Organized Play can't exist, since the Alignment rules are "entirely subjective" and could never be agreed-upon widely. The objective fact that Pathfinder Society somehow has managed to exist globally for years despite this obviously critical apparent flaw in the rules only goes to show that the Core Rules have an answer that is objective according to Official DMs, Developers, and Judges around the world.
Therefore, it must be ruled that the question of Acts-based Alignment versus Intention-based Alignment has an objective answer which is present in the rules, and that this question therefore is objective because there is an objectively-correct, rules-based answer to it.
Finally, the Question has a Mechanical Answer
The accepted answer shows that there is, in-fact, a mechanical answer, and cites the Core Rules as proof. The answer is well-defined in the core rules, which means that there is an objective answer to the question, which, in-turn, means that the question is not inherently subjective.