We can look at pre-modern anthropologists with some derision when we see that they often wrote that people who spoke a language without a future tense had "no general notion or intuition of time" (Whorf) or that European fusional languages are the perfection of morphology (von Humboldt). Before there was any systematicity in linguistics, it was common to make laughable racial or cultural statements about a people by judging the lexical or morphological traits of their language.
Thankfully, this clumsy methodology has been generally realized to be a farcical and pseudo-scientific, but vestiges still remain, particularly in the common conversation of grammatical gender. One doesn't exactly need to go looking to find moralistic indictments of the 'gendered' state of the English language (or any other language), along with the assumption that the 'patriarchal' status of our society is somehow determined or perpetuated by the fact we have gender-distinct words or markedness on feminine formants.
As it happens, grammatical gender is also the one area where linguistic prescriptivism remains an appropriate topic among open-minded persons. It would, among concerned company, be bigoted to correct a speaker for using a double negative or using a non-consensus form of an irregular verb, but the enterprise of correcting natural speech thought to be sexist (not in some explicit way, but because of 'unenclusiveness') remains something totally acceptable if not fervently endorsed by the mores of the day.
Markedness and Its Non-corollaries
Aside from that, the main question of grammatical gender is whether or not it transfers into grand social schemas, including the conceptual divide between men and women. The most concise response to this would be a calm 'no'.
Of course people who are entirely ignorant of other languages could be forgiven for thinking that there is any notable kind of social corollary of the distribution of nouns in a gender category. Chinese, Hungarian, Andean or Persian cultures are not gender-egalitarian because they lack morphological categories for gender; German, Hindi and French cultures are not mercilessly sexist because they have them.
In Indo-European languages, the feminine gender is usually linguistically 'marked' in that it takes special suffixation or agreement distinct from those of male, unknown or general entities. There are far fewer languages where the opposite true (Zayse-Zergulla in Eastern Africa for example), but there is simply no demonstrable social output of this. Languages with less markedness on feminine forms are not more egalitarian cultures and are certainly not 'matriarchal' societies (there are none). Quite simply, the morphology of a language is an epiphenomenon of millennia of diachronic change, not the cause of social mores, nor has there been any analyzable link suggested between gender markedness in language and cultural feminization.
Languages which distinguish past and present tenses must also necessarily have one form as a 'default' and unmarked form and the other as 'derived' and marked (analogous to masculine and feminine genders in IE languages). In English, the present tense is morphologically default, in Arabic, the past is default. This doesn't mean that English speakers 'privilege' the present over the past. In the same way, singularity and plurality are distinguished in many languages and singularity is nearly always the default form, but that doesn't mean that plural entities are marginalized and oppressed.
Of course we can make up ludicrous ex post rationalizations for why one form category is marked in English and not another: maybe English exhibits singular entities as default because its an 'bleak and atomist capitalist language that engenders the preferences of the rapacious individual over the collective'. Maybe we can say that English has unmarked present tenses because it 'disrespects the achievements of the cultures of the past and is only focuses in the immediate moment'. We can say a lot of ridiculous things about markedness, but they are absolutely no worse than saying that the existence of a masculine/feminine noun class distinction leads to misogyny.
Even a callous feminist should stop to wonder why, if language somehow conditions the relationship of men and women in a society, basically the same mosaic of male/female relationships exist in all societies of Homo sapiens while grammatical gender is only part of a small subset of the languages of those societies. An unbiased observed might surely remark that language is a reflection of how humans are predisposed to think, rather than thinking language (a property of the human mind) somehow precedes human thought. Of course admitting that human nature is primal to human culture is heinous in that it flips the whole social constructionist agenda on its head, and even worse means that you can run evil, sociobiological, 'reductionist' experiments on gender theory nonsense which is too hurtful for some people to even consider.
The Typology of Gender
Of course the very word gender has been subject to some unfortunate semantic shifts that have muddied the water anyway. Etymologically the term had nothing to do with sex or gender how we understand it, but was a catch all term for 'category' that began to be used to give a name to the different noun classes that existed in Indo-European languages. The historical accident is that one of these noun classes contained (along with rivers and the names of the winds) male humans while another contained (along with place-names and abstract nouns) female humans. So of the three Indo-European noun classes, one came to be called masculine, one feminineand the other neuter (< Lat. ne-uter 'not either').
Or what if there were a family of languages where there were two productive classes of nouns: one for women and abstract concepts and another for men and inanimate objects? If we put on our armchair structuralist linguist glasses and look for fanciful conclusions to reach, we might estimate that these languages were enlightened and feminine, and associated intelligence with the motherly instinct etc. etc. etc. Of course, this isn't the gender system of a noble-savage-type feminist utopia, but that of basically all modern Romance languages.
When an inanimate object is borrowed into a Romance language, it immediately is treated in the masculine/inanimate class while only females and new derived abstract nouns have the 'privilege' of taking the inflection of the feminine/abstract category (a privilege which is taken away in the plural when a feminine is infested by masculine company). (By the way, anyone can word any soulless phenomenon as a kind of social conspiracy.) There are of course many inanimate objects treated as feminine as well, but these are exclusively holdovers from Latin. All new inanimate objects fall into the masculine/inanimate class.
So what does this mean about the culture of post-Roman Europe? Nothing. It's simply an accident of derivational morphology and phonetic change. The masculine and neuter genders of Latin had merged because of the coincidence of their morphological similarity. Before that, the feminine gender of Indo-European split from a former 'animate' gender because of contact with a suffix which apparently had multiple purposes including deriving abstract nouns, denoting the collective category and of course marking female humans. Before that, Indo-European yielded two main noun classes: 'animate' and 'inanimate' which were highly pertinent to the active/inactive verbal system reconstructed for pro-PIE. What does this matter for gender relations? Not a jot or tittle.
The Anatomy of Political Correctness
It shouldn't be a surprise to anyone that the impetus behind a movement to political correctness isn't so much silly as it is incoherent. The newest fad in western languages is of course attempting to engineer language into being 'gender neutral,' which depending on the circumstances can mean two diametrically opposed processes; take the examples of English and Spanish.
In English, we've seen gender-divisive words like waiter and waitress being replaced by a form server, or fireman and firewoman being replaced with firefighter. This serves to neuterize gendered terms in to one general term, supposedly in a step on the glorious road to gender indistinguishably.
In Spanish on the other hand, the PC option is the exact opposite: that is, feminizing traditionally common terms and reinterpreting the original form as exclusively masculine. It's common to see presidente rendered as presidenta for female presidents or jefe 'boss' as jefa. For all of the history of Spanish, presidente and jefe were common gender (meaning they bore no gender morphology and could be used with women or men depending on the context), but now the impetus of linguistic engineering is to take unmarked forms and make them more marked, thus creating a wider area of distinction between the masculine and feminine genders in Spanish.
Thus the dictates of political correctness are to create more gender markedness in Spanish, while less in English. It seems like the only commonality is a disappointment with the status quo. I wouldn't be too surprised that if we lived in an alternate universe where feminists spoke Chinese or Hungarian, that they'd be rallying for grammatical gender, maybe just because they want special feminine forms. Who knows? One minute English is cruel because it has too many gender distinctions in pronouns, the next some disgruntled Tumblrite is demanding that every obscure sexual identity have its own special pronoun. Of course I might be biased in general because the very idea of gender-marking Latin 3rd-declension common nouns makes me want to vomit blood.
In the same vein, in college I recall reading a Spanish textbook which thought it pertinent to note that in Spain, a husband is called a marido while a wife is simply called a mujer, which is the general word in Spanish for woman. Obviously the textbook writers took this as a sign of blatant sexism against women, misogyny, male privilege, etc. and remarked on its unfortunate use.
It was particularly funny to me, seeing that only a year before I had had a conversation with a Latin teacher of mine (who was the chair of the women's studies program) on the same disparity in Latin, which existed in the other direction. She took the fact that there was a special word for wife uxor and none for husband other than the general word for man vir, as clear evidence of an oppressive masculine culture. Yes that's right; you can reach the same conclusion from opposite evidence. Whenever there is a gender distinction it must be sexist, and regardless of the directionality of the distinction, women are getting the short end of the stick. Direct counter evidence be damned.
When it comes down to it, there's no need for methodology or rigor for those who support the linguistic engineering of gender 'neutrality'. There's no need for consistency when the conclusion has already been made and dissent is dispelled by moral intimidation.