You're right that there is little difference between a corporation that one is de facto forced to interact with, and a bona fide government. For example, one can easily reframe USG as a corporation that you form a contract with by owning land, renting, or being on a public way. This does not mean that our current society is a libertarian paradise.
Turing completeness shows us the ouroboros of expressivity with programming languages. It's unfortunate people let their guard down in other areas.
https://en.wikipedia.org/wiki/Right-libertarianism
https://en.wikipedia.org/wiki/Libertarianism_in_the_United_S...
https://en.wikipedia.org/wiki/Objectivism_and_libertarianism
On the other hand, left-libertarians oppose capitalism while supporting personal property rights. Left-libertarians and right-libertarians find common ground in rejecting authoritarian governments.
https://en.wikipedia.org/wiki/Left-libertarianism
Libertarianism comprises a diverse collection of views that aim to advance individual freedom, and anyone who is not an authoritarian is likely to agree with some libertarian principles.