In recent years, libertarianism has become increasingly divided between thin libertarianism and thick libertarianism. Thin libertarianism only focuses on greatly reducing the size of government, upholding property rights, and upholding the non-aggressional principle (NAP), and is generally agnostic on all other issues. Thin libertarianism does not care about what attitudes people out there hold about social issues, and does not care about whether social liberties actually increase or rather become more restricted as a result of libertarian policies. Thick libertarians believe in the same governmental policies as thin libertarians, but they also insist on culturally encouraging everyone to adopt a live and let live attitude, and to rid society of traditional prejudices like racism, sexism and homophobia, so that individuals in society can truly experience an increase in liberty.
While moral libertarianism is not the same as political libertarianism, and indeed moral libertarians do not have to be, and are indeed sometimes not, political libertarians, moral libertarianism shares some of the core ideology and historical cannon of thought with political libertarianism. Therefore, moral libertarians can certainly be inspired by debates in political libertarianism, and vice versa. Looking at the matter from a basic perspective, it would appear that moral libertarianism shares some of the attitudes and goals of thick libertarianism. In particular, unlike thin libertarianism, both thick libertarianism and moral libertarianism share a concern about increasing individuals' liberty in practice. I believe that there is a lot in thick libertarian thinking that can inspire moral libertarians in this area, and vice versa. In fact, on social (non-economic) issues, moral libertarianism and thick libertarianism often take similar views.
Thin libertarians often accuse thick libertarians of taking the same stance as the increasingly authoritarian 'new left' on social issues. It is not uncommon to hear from conservative-minded thin libertarians accusing thick libertarians of having cultural Marxist sympathies. I believe that the moral libertarian principles, particularly the equality of moral agency (EMA), can help illustrate why the aforementioned observation is wrong. I have written extensively on how moral libertarianism almost never actually takes the same stance as 'new left' socialism on social issues. In fact, when explaining and promoting moral libertarian positions, I have encountered plenty of hostility from the left, thus proving how different our views really are. Moral libertarians support everyone in society having equal moral agency, i.e. to live as per their own moral compass, and oppose any kind of moral coercion. Therefore, by definition we have to oppose traditional prejudice taking away the fair share of liberty and equal opportunity due to women, racial minorities and LGBT individuals. However, an important thing is that we also hold the same attitude towards religious conservatives, for example, again because by definition we have to. We believe that the religious conservative should be able to hold, promote and live according to their views concerning marriage without prejudice from the rest of society under any circumstances, for example, and this right should have no expiry date. I don't think many 'authoritarian leftists' would hold the same view.
Thin libertarians also sometimes accuse thick libertarians of promoting social views that will inevitably lead to bigger government. For example, they sometimes say that thick libertarians promote libertine attitudes that cause family breakdown and increase drug and alcohol use, which will end up causing more welfare dollars to be spent, and therefore also more taxation. This kind of attitude is actually inconsistent with the general tradition of liberalism and libertarianism, in that we should not support restricting liberty just to pre-emptively prevent social consequences we may not like. Otherwise, it would be not be liberalism, but conservatism, socialism or something similarly authoritarian. Also, there is nothing under thick libertarianism that does not allow one to promote family values and clean living. Moral libertarianism goes even further: it insists that conservatives should have just as much right to promote their views as everyone else, without any social penalty.
In fact, a lot of conservative thin libertarians' accusations towards thick libertarianism betray their lack of faith towards liberty, towards what choices people would make if given full moral agency over their lives. There are even so-called libertarians who savour the prospect of a future where the complete division of the world into privately-owned gated communities (most if not all owned by conservatives, according to their logic) will mean that most people will live according to conservative rules, not because they want to, but because they are forced to by the property owners. How is this different from authoritarian conservatism? Both political libertarians and moral libertarians can support conservative positions, but they must still respect other individuals' equal liberty and moral agency in the process. Just like everyone else, conservative libertarians can make their case in the free market of ideas, and try to pursuade more individuals to live the way they want. Nothing more, nothing less.