Moral libertarianism sounds simple. And it really is. After all, it's simply about making sure that everyone has equal moral agency. And the only practical and logical way to do that is by allowing everyone maximum liberty to live according to their moral compass, and not allowing anyone the 'liberty' to prevent others from living according to their moral compass. A really simple concept that can be easily applied to almost all social issues out there (economic issues are often a bit more complicated).
Unfortunately, it isn't always easy to uphold moral libertarian principles. The classic case concerned opposition to unjust wars. For most of human history, when leaders of a country have declared war on another country, for any citizen to dissent was almost akin to treason. No amount of religious moral conviction was enough justification for allowing dissenters to speak up. Fortunately, this all changed somewhere around the 1960s, triggered by the Vietnam War. On a more everyday life level, social pressures still exist in many circles, limiting the political stances one can publicly take without social penalty. For example, after 15 years of fighting for marriage equality, I still find it difficult to raise the subject with many friends and family members.
The left in the West, ideological descendents of the enlightenment, has traditionally been a reliable champion of free speech, and the Free Speech Movement of the 1960s was instrumental in finally allowing dissent in a wide range of areas, most importantly regarding whether a war is just. However, in recent years, parts of the Western left have walked away from free speech, instead preferring an approach where people's feelings come first, the so-called safe speech. This climate has made staying true to moral libertarian principles very difficult indeed in some leftist circles. Throughout history, conservatives have sometimes made dissent a crime against loyalty, religion or traditional values. But making unpopular opinion a crime against individuals' feelings is indeed a new concept the moral libertarian has to defeat.
A moral libertarian must speak up according to their true beliefs, and must resist peer pressure to shut up. But since the moral libertarian wants everyone to be equally able to speak up freely, we must also aim higher. It is unrealistic to expect everyone to be willing and able to resist peer pressure in the way we do, taking social penalties left, right and center as a result. Therefore, we need to strive to change the culture itself. We need to bring about a culture where it is everyone's right to speak as they sincerely believe. We also need to promote the idea that people should not take offense in the face of disagreement.
Of course, just to bring about such cultural change would put us into conflict with much of both the right and the left. I have to say that it is not a particularly friendly climate out there for us right now, for parts of the right still believe in controlling language to preserve traditions (hence, for example, their opposition to marriage equality), and the left is increasingly walking away from liberty and rationality towards group-identity and feelings. But if we believe in the ideal of equal moral agency and a genuinely free market of ideas, there is no alternative but to face the opposition and make our case.