On Neoliberalism and Libertarianism

What is "Neoliberalism"?

Neoliberalism (sometimes called "Libertarianism") espouses the idea of  individual liberty=liberty of capital but it's reality involves state and international organisations, principally the World Bank and the International Monetary Fund, commanding their own economies and those of developing countries in order to decrease environmental and labour regulation in a "race to the bottom"  to minimise the labour costs of businesses in favour of cheaper production of goods.
One of these methods is to lend money to developing countries with the proviso that these countries deregulate their economies. 
This is happening in the UK and USA with the introduction of private prisons and immigration detention centres. Also, the so-called "Foundation" hospitals, "Free" schools and "City Academies" in the UK. These are run by private companies and individuals but receive government funding.
If anything, these programmes represent an increase in centralism and a decrease in local accountability. UK Academies receive their money from central government but are not accountable to local authorities like the existing state comprehensives are.

Neo-liberalism also involves denying or restricting the rights of workers to organise unions, the UK has laws against sympathy strikes and the current Conservative government is trying to limit the way unions can vote on strikes by insisting on higher turnouts. The marketization of higher education has increased with students facing higher debts (while) receiving fewer guarantees of a graduate job and no improvements in the learning experience.

To add: the realities of neo-liberalism include perpetual war and the denial of many individual freedoms. Possession of drugs is prohibited as is prostitution. Other non-violent offenses can land one in prison, including the "offense" of moving to a country of one's choosing to escape war, persecution or simply to better oneself.
Nonsensical and even racist terms are used by governments and their media allies like "illegal immigrants" and "welfare dependants". Or see George Monbiots' summary/essay:

https://www.theguardian.com/books/2016/apr/15/neoliberalism-ideology-problem-george-monbiot?CMP=share_btn_tw

Nations who defy neo-liberalism face interference in their political structure/processes, economic blockades, the propaganda war and even outright invasion in the case of Iraq. Libya, Iran, Russia, Ukraine, Venezuela and Syria have also faced the consequences of their defiance.
Secret trade deals like TTIP allow corporations to sue governments for enacting laws that intervene in their profits therefore it is not liberal, it is not progressive and it is definitely anti-democratic.
Liberals believe in the democratic process, only rabid Randians/Objectivists (alongside Neo-Conservatives) think intervention is acceptable and the idea of national sovereignty dates back to the treaty of Westphalia at the end of the Thirty Years War.

Libertarianism and Marxism.

Both are really offshoots of classical 18th century liberalism so there really ought not to be any conflict. For example liberalism rejects unnecessary taxation and government, at least in the absence of universal suffrage.

Marx talked about the exploitation of surplus labour. This means a worker is paid enough to keep him alive but he/she has to spend most of their time doing so while the capitalist keeps the surplus in the form of profits. Or put simply, the reason working hours are so long, and why businesses always complain about the minimum wage and limits on working hours, is so your surplus labour can be turned into profit.

Strictly speaking, capitalism is no different from slavery or feudalism but it claims to be voluntary as workers can always look for alternative employment unlike a serf. Of course, the big unanswered question is why does the capitalist "work" if he doesn't need to? This is always the argument about "welfare payments discourage people from working", but the amount of money required to buy even a small company would set anyone up for life. Therefore, there is more to "work" or labour than simply personal survival.
This would all work OK in some kind of fantasy world but often there just isn't enough work to go around because other people will still allow themselves to be exploited. Not only that: even if you are made redundant because your labour is no longer profitable then you are still technically being exploited, unlike say a freed slave.

The other argument is simpler: some "libertarians" focus on the big bad government telling businesses and churches what to do but there is a flip side to this: why is it OK for business and religion to tell the state what to do by influencing policy? Especially when all they do is tell people what to do all the time and governments at least have the veneer of democracy. I suppose this is why I'm an anarchist but also why there should be no conflict between libertarianism and Marxism.

Conservatism and Leftism.
Short comment based I have to admit on my own observations, experiences and a re-reading of the Unabomber Manifesto. I think politics can be explained by dividing society/voters/activists into two broad philosophical camps: Leftist-Egoists and Conservative-Collectivists.
Leftists* (or liberals) will not support a platform consisting of 99 proposals they agree with if there is one proposal they strongly disagree with**; whereas Conservative-Collectivists will vote for UKIP or Donald Trump (or George Galloway) on the basis of the one key policy that outweighs all the other policies that would normally make a candidate unpalatable.

*As defined by Theodore Kaczynski "Industrial Society and its Future" aka The Unabomber Manifesto; specifically his comments on leftists and liberals
**See, for example, Murray Bookchin "The Ghost of Anarcho-syndicalism"