Several years ago, near the start of my feminist awakening, I felt a yearning to get to know Heavenly Mother. I did the standard thing we do in the church when seeking revelation. I studied the scriptures, I pondered, and I prayed for guidance. The response - chirping crickets and a rolling tumbleweed. Nothing. So I kept at it.
We have little to no revelation explicitly detailing her existence. The most we have is the hymn "O My Father" which basically says that her existence is a logical extrapolation of our doctrine on eternal families. The scriptures state that it is essential to know God to inherit eternal life.  We also believe that the purpose of prophets is to teach about God. If we have no revelation on the subject of Heavenly Mother, we can conclude one of two things. She doesn't exist, or she does exist, but knowledge of her isn't important to our salvation (i.e. she isn't God). In my book, a subordinated or nonessential female deity is much worse for feminism than a nonexistent female deity. It gives the appearance of a divine imprimatur to female subordination on earth.
I believe in God. I always have, even though I wasn't raised in a religious household. The God I believe in is radically egalitarian.
There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus. And if ye be Christ’s, then are ye Abraham’s seed, and heirs according to the promise.I consider myself to be a liberal feminist, as opposed to a radical feminist. (The short version is that liberal feminists want to integrate women as equals into existing male-dominated spheres, and radical feminists want to create separate female-dominated spheres.) I also reject gender essentialism in all its forms. There aren't male virtues and female virtues- there are just virtues. We don't need a female deity to teach us how to be good because goodness isn't different for men and women.
Some say that a belief in Heavenly Mother is comforting because a female deity is better able to understand uniquely female concerns. I find this problematic. God is all powerful and all knowing. The Atonement of Jesus Christ is infinite and all encompassing. Stating that a male God cannot understand female concerns is to deny the omniscience of God and the power of the Atonement.
As I continued my studies, I came across two interesting things. The first is that in the scriptures, Christ often refers to Himself using maternal imagery. He pleads with Jerusalem and offers to gather them as a hen gathers her chickens.
The second is a beautiful quote by Chieko Okazaki on the majesty and universality of the Atonement and how it's an individual experience. It's quite lengthy, but it's worth reading the whole thing.
[H]e knows what it felt like when your mother died of cancer- how it was for your mother, how it still is for you. He knows what it felt like to lose the student body election. He knows that moment when the brakes locked and the car started to skid. He experienced the slave ship sailing from Ghana toward Virginia. He experienced the gas chambers at Dachau. He experienced napalm in Vietnam. He knows about drug addiction and alcoholism.
Let me go further. There is nothing you have experienced as a woman that he does not know and recognize.
On a profound level, he understands the hunger to hold your baby that sustains you through pregnancy.
He understands both the physical pain of giving birth and the immense joy. He knows about PMS and cramps and menopause. He understands about rape and infertility and abortion.
He understands your mother-pain when your five-year-old leaves for kindergarten, when a bully picks on your fifth-grader, when your daughter calls to say that the new baby has Down’s Syndrome. He knows your mother-rage when a trusted babysitter sexually abuses your two-year-old, when someone gives your thirteen-year-old drugs, when someone seduces your seventeen-year-old. He knows the pain you live with when you come home to a quiet apartment where the only visitors are children, when you hear that your former husband and his new wife were sealed in the temple last week, when your fiftieth wedding anniversary rolls around and your husband has been dead for two years.
He knows all that.
He’s been there.
If people find it meaningful to think of God manifesting in female form, fine. It's the same sort of thing as painting Jesus as a different race. If those thoughts draw you closer to God, then who am I to argue. But when I sought Heavenly Mother, I found Jesus. And praise be to God for that revelation.
 The line is "In the heavens are parents single? No, the thought makes reason stare. Truth is reason, truth eternal tells me I've a mother there."
I don't consider the reference to heavenly parents in The Family: A Proclamation to the World to be dispositive because when President Packer referred to it as a "revelation" in an October 2011 conference talk, the published version was changed to refer to it as a "guide". Therefore, it is safe to conclude that whatever the status of that document is, it isn't a revelation.
 See John 17:3
 For the purposes of this post, the term "God" refers to the Godhead, either jointly, or to one member of the Godhead.