Don't be fooled by powerful people who claim to be libertarian, but are actually only interested in promoting freedom for themselves while denying the same to others.
Your second paragraph is setting up a false dichotomy. It's not the corporation xor the state. Fundamentally, corporations as we know them are creatures of the state - government chartered legal entities, running on the government's legal system, with government granted liability shields. But the main point is that where the nominal state disappears, the corporation(s) step into the power vacuum and become the inescapable government. To be able to take your business elsewhere or create your own competitor, you need individual rights. While the underlying physics supports this directly for some abilities, for others you need coordinated collective action. This often takes place through the state, meaning that blanket calls to dismantle parts of the current government can often serve as cover for enabling newer less-constrained government. Think yin-yang and NP/Turing completeness circular reductions, not towering software builds.