I see a few tools used to show sexism in narrative. Used correctly, they can yield useful information, but used incorrectly, or maliciously, they show sexism anywhere the user wants to put sexism.
The Bechdel test is sometimes used to show sexism, but it's there to show one particular form of sexism, that of assigning parts in motion pictures. The ultimate purpose of the test is to increase the frequency of women in film and provide more job opportunities. The basic assertion is that if women are 50% of the population, they should get 50% of the visual representation across the entire industry. It's not there to show that any one film is sexist, its there to show that Hollywood has a sexist bias in the way that roles are written and assigned.
Agency is also used to show sexism in stories. What sort of agency does a woman have? Used well, the question opens up interesting inquiries. Used poorly, it becomes a bludgeon, insensitive to the very goal that it was intends to support.
The primary problem with agency as a metric is that agency exists within the context of a story, while the analysis can happen outside the context. With a loss of context, the tool becomes unreliable.
The second and even greater issue is that lack of agency doesn't correlate with sexism. Agency is used as a tool in many stories, sliding about, to increase and decrease the emotions of the reader. In many action genres, agency boils down to heroes and villains, where even the heroes find their agency challenged. Without a firm idea of genre, without a firm counting of how many male characters vs. female characters lose agency, the question of agency is likely to mislead you.
Objectification can also mislead for the same reason. Out of context, objectification can be seen as separating out women, but in context, these characters may suffer the same fate that many other secondary and tertiary characters face.
The Smurfette principle fails when the user fails to account for the status and importance of a woman in a story. Only if a woman is a universal embodiment of generic femininity among an otherwise diverse male cast does the part rise to the status of Smurfette. Women that are distinct characters aren't Smurfettes, even if they are the only woman. One woman among men isn't necessarily sexist.
The biggest issue is that these tests exist to detect sexism against women. While a noble goal, the failure of these tools to detect other forms of sexism leaves any analysis weaker than it should be. It stands to reason that the more forms of sexism that you can show, the stronger your argument that sexism exists. In many films, the sexism against women is often the weakest and most difficult to show style of sexism, while the sexism by men against men is rampant and easily documented.
A focus only on women means that superficial changes can be applied to films that make the film seem less sexist, but really makes the situation worse. Such an approach has led to the rise of the "strong woman" in film, one who's functionally a bland and an otherwise forgettable character. Such a change is not a real improvement as strong woman are written to seem empowering but more importantly, they are written to avoid offense. In essence, one has changed one stock, interchangeable character for another. At least a stock, sexist woman gets to spout a different point of view containing a different ethic.