A gender role would be anti-libertarian only if a government used resources or created policies for the purpose of supporting or opposing that gender role.

Just because a few women have felt limited by gender roles does not mean all women have. Many women have and do look up to and model after other women, and have taken on a gender role and are very happy. Diversity should be celebrated, not shamed.

For example:

"Part of me, whether due to biology or culture, will long for a big strong man or government to keep me safe. But a bigger, better, stronger part longs for the freedom to make my own way."

Is there something necessarily wrong or unlibertarian to desire to be protected by a big strong man? I would think that this is something entirely different from desiring to be protected by coercive government.

My biggest worry is that in making these comparisons, we might be perverting something we shouldn't be. It seems that Cathy goes beyond criticizing gender roles per se and criticizes the actual content of the gender roles: that it is worse for a woman to be protected by a man than solely by herself.
My recent post The Expression of the Total State: Prison

It's from Charles Johnson's artile "Women & the Invisible Fist"

Consensual rather than coercive (when “spontaneous” means “uncoerced”);
Polycentric or participatory rather than directive (when “spontaneous” means “unprompted”); or
Emergent rather than a consciously designed pattern (when “spontaneous” means “not planned in advance”);

Sexism has the latter 2 characteristics of a spontaneous order, but that doesn't mean it's uncoercive (which is the classical pseudo-libertarian argument against "gender" feminism). An invisible fist still make your face swell even if it's unseen.

Mine apology if I cause any misunderstanding.

There is a misunderstanding rearing its ugly head here.

I am all for Cathy's argument for individualism against gender-roles. Gender-roles, as Charles John argues somewhere can spontaneously arise without state coercion, but that does NOT make sexist gender-roles "libertarian" because gender-roles clearly restrict men & women's aspirations & actions.

That's why I called those who support gender-roles "pseudo-libertarians," & substituted "state" with "man" to show them how statism & sexism are evil twins.

Regards!

"My version of libertarianism is based on individualism."

There, fixed that for ya.

Cathy said nothing of the kind. She is asking for allowing people to be whatever they want to be. This comment reveals more about you than Cathy.

Shaun, you seem to have a limited vision of what libertarian principles involve. Libertarianism is based on individualism. Philosophical individualism implies that each individual should be judged on their own merits, not on stereotypes, whether gender. race, age, or ethnicity or any other such category. Sexism of the kind Cathy speaks of violates that individualist principle.
Perhaps you are unaware of the history of libertarian thought. I recommend George H. Smith's book The System of Liberty.
However in an essay in progress for the libertarian feminist anthology that Ross Kenyon and I are editing, I have an essay on libertarian feminist theory (with Charles Johnson). Herei s an excerpt on the individualist basis of libertarianism:
"Individualism is at the heart of libertarian theory and has been from the beginning. The classical liberal tradition of Mary Wollstonecraft, John Stuart Mill, and many others that influenced early American libertarians was philosophically individualist. Wollstonecraft, according to one scholar, was the one who “established the individualist roots of equal rights.” She in turn influenced many of the women’s rights activists as well as the libertarians. “Like Wollstonecraft,” writes women’s studies scholar Josephine Donovan, “Stanton believes that ‘nothing adds such dignity to character as the recognition of one’s own self-sovereignty; the right to an equal place, everywhere conceded—a place earned by personal merit.’” In his radical treatise On the Subjection of Women, Mill proclaimed:
The modern conviction, the fruit of a thousand years of experience, is, that things in which the individual is the person directly interested, never go right but as they are left to his own discretion; and that any regulation of them by authority, except to protect the rights of others, is sure to be mischievous.
Though Mill may not have been thoroughly individualist, as some feminist critics have argued, it is his individualism that has left its mark on American libertarian thought while it is Wollstonecraft who left her mark on the individualist and libertarian feminist tradition.

The American libertarian tradition, inheritor of this classical liberal thought, included libertarian writers such as Thomas Paine and David Thoreau, as well as anarchists such as Josiah Warren and Voltairine de Cleyre, who were all thoroughly grounded in individualism. Warren, America’s first anarchist, says historian Ann Caldwell Butler, based his anarchist ideas on the concept of individualism. Warren, she writes:
..insisted that these laws [of nature]teach us that our own happiness depends upon a proper respect for the happiness of others and that therefore we should not make social arrangements which require compulsion or the violation of the natural freedom of any individual. … The sovereignty of every individual over his or her person, time and property must be preserved.
De Cleyre asserted that individualist anarchism was the logical extension of the American libertarian tradition in her essay, “Anarchism and the American Tradition.” In stressing the importance of individual freedom, she wrote: Anarchism, to me, means not only the denial of authority, not only a new economy, but a revision of the principles of morality. It means the development of the individual as well as the assertion of the individual. It means self-responsibility, and not leader worship.
Like Warren and de Cleyre, other anarchists saw individualism as something that stressed self-responsibility, not just rights. "
Please note especially the quote by Josiah Warren. Sexism and gender role stereotypes harm the individuality of both women and men by attempting to straitjacket them in only the roles that some approve rather than what individuals themselves may wish to be. Cathy's essay is thus entirely within the purview of libertarian theory and principles.
{quote copyright 2013 Sharon Presley]

another important reason feminism should be relevant to all libertarian thought is its analysis of how cultural attitudes make violence and aggression normal or acceptable. there are very few people who do not identify as feminists of one type or another who are interested in examining and addressing the phenomenon of victim-blaming. virtually all people who identify as libertarians are concerned with the issue of victimless crime, and many of them will often engage people who say "well I don't think substance y should be illegal necessarily, but if person x did not want to be arrested or harassed by the police, fined, or maybe even jailed, then they shouldn't have had it on them–they should've just followed the law!" and vigorously try to dispel their notion that individuals being prosecuted for such victimless offenses are guilty of a crime and demonstrate that those charged with victimless offenses are in fact victims themselves. many of these same people however apparently do believe that dressing in a certain manner, going over to someone's house or into their bedroom, being intoxicated, having a history of promiscuity–and the list goes on and on and on, to the point where it pretty much extends to nearly any behavior whatsoever that is convenient enough for the real aggressor in each situation to point to–must indeed have an ostensible "victim" and that those guilty of them are deserving of punishments ranging from sexual harassment to rape. just because the police are not the ONLY group who perpetrate a specific form of aggression, does NOT mean that it is not aggression. the feeling (which I have found to be common among other "libertarian" men my age) or intuitive sense that aggression can only be committed by the state and that acts of violence or aggression by other groups can be extenuated by the personal (and always victimless) choices of the victims themselves is not a fair or rational thinking-through of the NAP, but rather a very emotionally founded conviction that arises from the enjoyment of the privileges (i.e., the ability to commit or condone acts of aggression without having them be seen as such) they are afforded by such attitudes. most of them like to smoke pot, of course, so then they are fine with employing the language of "victimless crimes" and showing how just because some individual, group, court, organization, etc. has deemed a certain substance prohibited does not justify the that a person should pay monetary damages at best, and at worst experience the caging, harassment, humiliation, and dehumanization that the legal apparatus proscribes.

"Libertarianism is about using violence on people"

you mean to say "NOT using violence on people"? Or More specifically "Not initiating aggression according to a specific set of property norms, on people"?