The Genderless Spirit
Spirituality, a constant unconditioning of your soul, slowly pushes you to your true identity, the Self — which is genderless. So it doesn’t come as surprise that there will be some reckoning regarding the feminine and masculine principles (Siva and Sakthi) that operate within you, as well as in the world. Sometimes it just happens without knowing (as in genuine bhakti), and sometimes through critical reflection, or as in my case bit of both.
I want to stress that this is not about males becoming female or vice versa. It is about just allowing the evolution of the masculine and feminine principles in each of us. Like Amarananda Bhairvan mentions in his Kali’s Odiyya, as well as the Yaqui Indian shaman Don Juan: sexual identity is so strong that people cling to it as if their lives depended on it.
I sometimes have this perspective where I believe that Reality is not in some “higher plane”, but it is here and now, such that the experience of Reality is really more about acceptance or awareness (or understanding). You cannot experience the substance or essence of life in its fullness when you’ve got an entire other half of traits that are very underdeveloped. I think the very act of acknowledging it and the desire for it automatically paves the way for it and opens the doors greatly for it to take root and grow.
Society
It is not only important to one’s own evolution, but for society as well. Like contemporary bhakti saint Mata Amritanandamayi said, the world is screwed up (those are my words :)) because of the imbalance between masculine and feminine powers — being dominated by the masculine. If people want to reduce the conflicts in the world (ranging from bad governance, to wars, to broken families, and high crime) a good root cause analysis will show this is the root of all problems. Over ninety percent of the worlds crimes are committed by men — and yet men are treated as the wiser, the more controlled, and stronger. This shows a serious flaw and imbalance in culture and human thought, worldwide.
In the past, in many of the native spiritual cultures spanning continents, it is the women who were the great spiritual masters and leaders. This is probably because for women the kundalini is active right from birth, whereas in men it is dormant. Probably also matriarchy itself is about cooperation and synergy, rather than a divisive and power based structure of patriarchy. And also like anything which offers freedom (like democracy), it can be taken advantage of by those who want power and have no regard for equality and fairness. But the need for the balance will all come back… catalysed every now and then by leaders who propel the issue. All driven by necessity (man is too preoccupied in greedy pursuits to be awakened by anything other than necessity, the great harbinger that brings about change).
Genetics
It’s all just too easy to observe how girls play with dolls, and boys with mechanical things. How girls cooperate and compromise, and boys compete for winner-take-all. And so on. Just how much of masculinity/femininity is really tied into one’s gender (or genetics for that matter)?
Maybe a lot of the feminine/masculine traits are inherited over 6 million years of human evolution, and far more if you include our evolution from the animal kingdom. But the question is, is it immutable, or can it reprogrammed, de-conditioned, or unlearned (or conversely, balanced so as to become whole)? I’d say yes it can be unlearned/learned. As unlike the other animals, human beings are beings capable of reflection and self-analysis — meaning we can make the choice to evolve to something more than what we are born with. When we integrate the feminine and masculine principles within us, is when we really move beyond animals, to the Rama, Krishna, or Buddha. In the process of striving for that goal, the Atman, we grow into more evolved sentient beings, and a better society.
I don’t think a man can acquire feminine traits in total (and vice versa), as still there is the factor of prakriti – the material constituent and the intelligence/driving-force of the universe and all beings in it (which includes chemicals, genetics, what we eat, what we breath, etc.), which will drive us each differently. But there is a tremendous gap to be filled, and it can be filled.
I look at it as (not really the best example I can think of for now) not much different than the choice of becoming vegetarian (assuming for a moment that we’re from cold/frigid climate, which had driven us to become meat-eaters for most part of our evolution). So if even such people can make conscious spot-choices that can make us change counter to what we’ve been programmed [to eat], then why not in the other traits as well? Non-vegetarians could argue that that’s the way it is: that it is part of our nature to be meat-eaters. But the very fact that we can make a conscious choice (to evolve, unlike lower animals), only goes to show that it is not “in our nature”.
Shiva-Shakthi / Radha-Krishna
I believe one of the things necessary for spiritual growth is for men to develop femininity, and for women to develop masculinity, so that in the end they are “complete”, and exhibit the traits of the Atman (or a divine manifestation of the Atman, like Krishna).
In most cases, the development of femininity occurs naturally with sincere spiritual practice. However there are small number of esoteric spiritual traditions which had an approach where they would bring out the femininity in the males very explicitly. For example, the spirit master would strive to bring the femininity out of the man through all sort of rigor such as: live among women, acting like them, dressing like them, engaging in feminine activities, and acquire feminine (not female) traits like: receptivity, compassion, integration, acceptance, compromise, uninhibited expression (as opposed to repression) of feelings (of love, happiness, pain) through many means (singing, dancing, crying, nurturing ones artistic talents – painting, music, poetry, story writing).
The purpose of the exercise was not in as much to transcend gender conditionings, but to transcend any conditioning in general. A constant unlearning, in preparation for seeking or “stalking the spirit”.
Because of its rigor, directness, and the mental stamina it needed it, it was reserved for only a few, and called the “left-hand” path of God. But I feel the time for it is coming… to become the “right-hand” path of God. Necessity will be calling out for it sooner or later… just as it called out for yoga to be revived and spread.
Probably femininity and masculinity studies should even be part of high school curriculum. I’m talking about some serious treatment of the subject which will cause each gender to reflect on themselves. One doesn’t even have to study these differences (given the hectic pace of life), but even a basic acknowledgement is a major step in allowing those missing traits to take root in oneself.
Take a look at the two adjacent pictures — of Krishna and his brother Balaram, one can see a certain degree of femininity in the way Hindus portray God in male form. Spirituality is about attaining that level of internal gender balance. And by the way, before anyone gets any ideas… just because I’m addressing the need for femininity in males (and vice versa), I’m not gay; I am perfectly straight. This has nothing to do with sexual orientation.
How often is it that men complement their wives for their selfless compassion. Who in turn take it all in, saying “that’s what makes us women”. I still wonder just how much of it is total conditioning and how much is genetic. Regardless, my point is, as long as man does not give his share of compassion, he’s not going to give it to the world either, and the world power structure being dominated by men, will cause the world to remain in its present state of imbalance for a while. This will change when women start challenging this, requiring men to reciprocate their share as well. Femininity having a tolerance and compassion is one thing, but to have it consistently exploited is another matter. Note, to emphasize again, this is not about men vs women, but about men/women each seeking balance. That is, evolving by moving towards the genderless Atman (as idealized in the above pictures), else any sort of worship is a feeble attempt at most (and hypocritic for the serious spiritual aspirant).
Hindu ithasas and puranas are not immune from gender stereotypes. At the same time I feel what they contribute in terms of restoring balance far outweighs the stereotypes they introduce. For example, just take a close look at the pictures on this page. 
Three out of four of these pictures reflect a type of feminine-masculine (almost genderless) principle that society lacks and can really benefit from. Even the image on the below, of Lakshmi rubbing the feet of Ananda-Padmanabha Vishnu, is in itself nothing wrong — as long as it is counterbalanced by at least some images of the reverse. And who will do that? the liberated men and women of the future. See that picture above, with Krishna rubbing Balaram’s feet? Someone will paint a picture with Balaram replaced by Radha. That there is not even one such shows to go just how entrenched, subtle, and unchallenged gender stereotypes are even in our spiritual literature that strives to transcend the very same.
Liberated men and women should seek to balance the errors they see with opposing images. Using creative solutions, not destructive, to counter balance anything. I’m sure it will happen, with things like yoga, as man awakens to femininity, and women more liberated. Hinduism is not fixed by anything, it evolves. It is not a thing you destroy nor can destroy. 
Like the Gita says, that which has no beginning, has no end, and so how can it be destroyed. It’s amazing how some folks try to still tear down anything Hindu, and while never failing to expropriate knowledge from it. These images for example in today’s new age or pop-culture parlance would termed as guided imagery or biofeedback for self-improvement.
As a side note, I always found it amusing to watch some colleagues in the USA, especially from heavily male-dominated (and female-subjugating) religions, cringe when they see pictures like that on the right (I had a small Kali photo, and also a small photo of my local Murugan deity, in my office). In the picture on the right, God (in female form, as Durga) slays the shape-shifting Mahishasura demon (representing the ego that gone power-hungry).
One final note: I really don’t care how these images came into being. I believe in the tradition of the itihasas (”thus verily it came to be”). What is is, is. Whatever has come to be has come to be because we caused it to be. Trying to analyze their origins would be useless. It simply is. But we do have the ability to creatively add to it (regardless of what past baggage it has), making the next “thus verily it came to be”.
“We are what we think. All that we are arises with our thoughts. With our thoughts, we make our world.”
– Buddha
Multivalency
Here comes my favorite word again! Multivalency. At one time I used to believe that the Atman is not necessarily genderless or androgynous, nor male or female — but all at the same time. That is, the Atman exists in the dual state of a Masculine-Feminine (Radha-Krishna, Shiva-Shakti) cosmic dance, not much different from the wave function or wave-particle duality of physics. But then when you think about, this duality was created by us, by creating one set of characters and calling it masculine and another set as feminine, modelled close to mirror our sexual identities, and our desire to understand the universe as the work of opposing forces. Or for that in order for desire itself to manifest.
Final Thoughts
My big question is how is it that such an important subject as this has not been treated more explicitly in spirituality, and is almost just left to the sidelines. After all, spiritual literature does indicate its awareness on the matter (in it’s images, symbolism, dance forms, poetry, etc.), just that it hasn’t become an explicit treatment. Maybe there just were not that many people who got to the maturity level that this path demands. I guess that’s why it’s the “left-hand” path of God, and that these left-hand paths happened to be matriarchal or gender-agnostic is no surprise. For example, in the [past] culture of Kerala, you’d find as many Aghorinis as Aghoras who moved about freely among each other without gender differentiation. Even the fact that Aghorinis turned out more often to be superior in their spiritual mastery, it was still gender-agnostic (it is only we who look at them as “matriarchs”), recognized for their value rather than the potential carried by their gender.
Exploring our selves along these lines will be very revealing and will expose wide open our holes, weaknesses, strengths, etc. Or maybe that itself is the reason why the sages deflected away from this — that too much reflection might result in one being preoccupied in the details, as opposed just striving to elevate the heart and mind via some form of less critical yoga, and letting it just happen, i.e. in the process of moving towards the genderless Atman. But how many people do this genuinely and sincerely? and how many more people to suffer while we evolve “slowly”? A catalyst will come — maybe as powerful women spiritual leaders (like in those once matriarchal societies), who will probably take the 20 million or so people practicing yoga to new levels… just a thought!