12 Let no man despise thy youth; but be thou an example of the believers, in word, in conversation, in charity, in spirit, in faith, in purity.
1 Timothy 4:12
The Church of Jesus Christ of Latter-day Saints can depend on left-leaning members to draw a growing demographic, which would otherwise be repulsed by organized religion, to learn about and even accept the Restored Gospel.
A religious "none" is someone who, during a survey, says that they have no religious affiliation. Nearly one third of young adults (ages 30 and under) are religious nones, according to a 2012 Pew Research Center survey. Most of you are probably not surprised by this fact if you haven't heard of it already. I've attended at least one or two Sunday School lessons or Priesthood meetings where this trend of increasing secularization was cited as proof of how wicked and evil the world is becoming. However, this is a flawed assumption and reading into the results tells a different story. The key takeaway from this survey is that the majority of this group actually still believes in God and that only a fraction self-identify, when pressed, as Atheists or Agnostics. The common consensus is that during their life, these "spiritual-but-not-religious" young people have drifted away from organized religion, viewing it as "judgmental, homophobic, hypocritical, and too political". While a vast majority are not actively seeking a new religion, they have not given up the spirituality of their youth.
The Religious Economy
Religions and believers have been compared to a marketplace where the former are selling a product (religious beliefs) and the latter are consumers (by attending church). When a believer no longer likes the product their religion is selling, then they will leave. Most of these religious nones are unsatisfied customers. Currently, they are not shopping for a new religion because they feel that every religion has the same political or intolerant mindset. As Mormons, we should recognize that our Church's political neutrality and gospel of love and tolerance fits a demand in the marketplace. When someone joins the Mormon church we don't require a political litmus test, the rejection of the science of evolution and global warming, or the intolerance of all things homosexual. Mormon liberals need to better market themselves in order to reach out to this group of religious nones and introduce to them the restored Gospel of Jesus Christ. If we don't, then we could spoil an opportunity to increase our "market share" in the religious economy.
(NOTE: If you are offended by Missionary work being compared to free market capitalism, then you might be a liberal.)
Coming Out of the Closet
It can be tough for Mormons to be outspoken as a liberal these days (or even a moderate conservative). As with any tight-knit social group, Mormons can sometimes think that if you don't think exactly like them, then you are not one of them. This is because what brings people together is what they share in common. I, for one, don't share political beliefs with some of my ward members, but I know that what truly brings us together is our common hope in Christ and the Plan of Salvation. In some cases, there may be a social price to be paid when you become the ward or branch's token Democrat. But the truth is that the vast majority of your conservative Mormon ward members do not care what your political beliefs are. And if they do, they may just want to have the occasional spirited debate on a given topic and then go back to loving and serving you as another member of the ward family.
So how do you become a good, liberal member missionary? I would recommend following the exhortation of Paul to be "an example of the believers, in word, in conversation, in charity, in spirit, in faith, in purity." I would argue that we shouldn't use our political views to fight conservative Mormons but rather to attract the "unchurched believers" by letting them know that the Church is politically neutral, that diversity exists, and that our shared common values are solely rooted in the Gospel of Jesus Christ.
 "'Nones' on the rise". October 9, 2012. Pew Research. http://www.pewforum.org/2012/10/09/nones-on-the-rise/#_ftn4