I don't oppose governments. I oppose some of their laws.
Most ordinary people oppose laws--half the country opposes the ACA, the other half opposes the Patriot act. Perhaps libertarians oppose more laws than the average person, but opposing laws and advocating full-on anarchy are two very different things. There is no hypocrisy inherent in calling for the repeal of some laws and calling for the enforcement of others, because this is what Democrats, Republicans, Greens, Libertarians, and all the rest of them do 7 days a week.
You reference Ayn Rand in jest but it is worth pointing out what she and other libertarian thinkers have actually said about the role of government:
> Such, in essence, is the proper purpose of a government: to make social existence possible to men, by protecting the benefits and combating the evils which men can cause to one another. - Ayn Rand
> The free society has an indispensable role for government. The law, in a society of free people, protects the life, liberty, and property of all persons alike, ensuring peaceful conditions within the community. Government performs as an impartial umpire, by interpreting and enforcing the previously agreed upon rules. - Ludwig von Mises
> A government which maintained law and order, defined property rights, served as a means whereby we could modify property rights and other rules of the economic game, adjudicated disputes about the interpretation of the rules, enforced contracts, promoted competition, provided a monetary framework, engaged in activities to counter technical monopolies and to overcome neighborhood effects widely regarded as sufficiently important to justify government intervention, and which supplemented private charity and the private family in protecting the irresponsible, whether madman or child -- such a government would clearly have important functions to perform. The consistent liberal is not an anarchist. - Milton Friedman
In fairness to you, there are some libertarian thinkers who have been more on the anarchist side (Murray Rothbard comes to mind). But there is nothing inherent in libertarianism that would require libertarians to adopt an anarchist position, and in fact most libertarian thinkers have taken a very positive view of government when it enforces those laws that libertarians think are important.
What I'm trying to say is, libertarianism isn't the same as anarchy, and most libertarians aren't working to destroy the government. They're working to change it, to make it better, the same goal that conservatives or liberals or anybody else has. And there's nothing inherently hypocritical about repealing drug laws but keep prosecuting thieves.