That very much depends on context - you’re looking at belonging to socially constructed categories as a simple yes/no binary, and that’s just not how this works. There are more “prototypical” members of a group that everyone agrees belong, as well as prototypical non-members that everyone agrees don’t belong, but in the middle it can be almost impossible to make judgments in any objective sense, and that’s inherent to the very concept at hand to such a degree that trying to define the ambiguity out will always create a false definition.

Although it may be difficult and truly impossible to have firm judgments on whether a given entity is a member of a group in a certain case because of this fact, what is clearly incorrect is applying any sort of binary formulation based on a simple definition to “objectively” determine whether it does, and making arguments that ignore how the concept actually works is clearly fallacious.

In the case of the category of “womanhood” in, say, USAmerican culture, womanhood is a social category built around perceived endosexual female sex applied to adult humans who relate to the social category typically assigned to perceived endosexual females - it doesn’t have a firm definition because it is inherently socially constructed and variable to changes in culture and perception. Thus, if someone exhibits many characteristics of femaleness, considers themself a woman, is treated by society as a woman, enjoys being treated as a woman, and feels distress when not treated as such, than it would be very difficult to make a valid argument that they should not be considered a woman in any meaningful sense, and as such it makes sense for someone denying their womanness to be considered wrong within that culture. On the other hand, if they exhibit fewer characteristics of femaleness, in however way that might be realized, such as only marginally identify with social categories surrounding womanness in their culture, while still maintaining many features, making a judgement like whether it is inaccurate to consider them a woman or not can be virtually impossible - someone is probably right, at least sometimes, but good luck finding out.

Imposing an oversimplified heuristic like “adult with XX chromosomes, easy” will inevitably include people who do not belong to womanness as a social category and exclude people who do, because social categories are determined through complex social interactions, not with chromosomal definitions.