I really think we're having a fundamental issue in terminology here. How are you defining gender? Especially when you say gender roles aren't part of gender?
This is what I am assuming you mean:
gender roles = social factors
gender = biological factors
However a_rec, myself, and Butler are meaning this:
gender = social factors and gender identity
sex = biological factors
The identity part is crucial.
Ye Old Wikipedia, the most scholarly of sources (Click to show)
Let's consult the most scholarly of sources, ye old Wikipedia:
"The World Health Organization defines gender as the result of socially constructed ideas about the behavior, actions, and roles a particular sex performs. The beliefs, values and attitude taken up and exhibited by them is as per the agreeable norms of the society and the personal opinions of the person is not taken into the primary consideration of assignment of gender and imposition of gender roles as per the assigned gender. Intersections and crossing of the prescribed boundaries have no place in the arena of the social construct of the term "gender".
The assignment of gender involves taking into account the physiological and biological attributes assigned by nature followed by the imposition of the socially constructed conduct. The social label of being classified into one or the other sex is obligatory to the medical stamp on the birth certificate. The cultural traits typically coupled to a particular sex finalize the assignment of gender and the biological differences that play a role in classifying either sex is interchangeable with the definition of gender within the social context.
In this context, the socially constructed rules are at a cross road with the assignment of a particular gender to a person. Gender ambiguity deals with having the freedom to choose, manipulate and create a personal niche within any defined socially constructed code of conduct while gender fluidity is outlawing all the rules of cultural gender assignment. It does not accept the prevalence of the two rigidly defined genders "man" and "woman" and believes in freedom to choose any kind of gender with no rules, no defined boundaries and no fulfilling of expectations associated with any particular gender.
Both these definitions are facing opposite directionalities with their own defined set of rules and criteria on which the said systems are based."
"Early gender identity research hypothesized a single bipolar dimension of masculinity-femininity—that is masculinity and femininity were opposites on one continuum. As societal stereotypes changed, however, assumptions of the unidimensional model were challenged. This led to the development of a two-dimensional gender identity model, in which masculinity and femininity were conceptualized as two separate, orthogonal dimensions, coexisting in varying degrees within an individual. This conceptualization on femininity and masculinity remains the accepted standard today.
Two instruments incorporating the multidimensional of masculinity and femininity have dominated gender identity research: The Bem Sex Role Inventory (BSRI) and the Personal Attributes Questionnaire (PAQ). Both instruments categorize individuals as either being sex typed (males report themselves as identifying primarily with masculine traits, females report themselves as identifying primarily with feminine traits), cross sex-typed (males report themselves as identifying primarily with feminine traits, females report themselves as identifying primarily with masculine traits), androgynous (either males or females who report themselves as high on both masculine and feminine traits) or undifferentiated (either males or females who report themselves as low on both masculine and feminine traits). Twenge (1997) noted that, although men are generally more masculine than women and women generally more feminine than men, the association between biological sex and masculinity/femininity is waning."
So yeah, it seems a bit misguided to parse "gender roles" out of gender as its own distinct thing, when in fact it's part of gender. Just as biological considerations are part of gender too. However there's also gender identity which sits at a crossroads here. There are some no doubt who still feel a distinction between biological sex and gender is misguided, but this is hardly something that is widely accepted. Causal links between biological factors like hormones and genes and certain behaviors have been demonstrated, but even the most diehard determinist would admit there's a long way to go before one can say there's a direct causal link between hormones and gender.