Alright, can we first agree that the non-aggression axiom is a bedrock principal of libertarianism?
No. The non-aggression principle leads to anarchism, but most libertarians aren't anarchists.But carry on anyway.
It doesn't
lead to anarchism. But some use it to justify anarchism.The basic principle is that it should be legal for anyone to do anything he wants, provided only that he not initiate (or threaten) violence against another person or legitimately owned property of another. So, in a free society, one has the right to manufacture, buy or sell any good or service at any mutually agreeable terms. And there would be no victimless crime prohibitions, price controls, government regulation of the economy, etc.
It does not rule out self-defense. It does not rule out communicating something that is emotionally hurtful, disturbing, hateful, disgusting or obscene. It also does not rule out persuasion.
The difference between anarchists and non-anarchists with respect to the non-aggression axiom is that non-anarchists believe a government can exist as long as there is a well-enforced constitution that sets out a narrow scope of government power. Essentially, the sole role of government is to protect the life, liberty and property of its citizens.
I'm going to have to get back to abortion later.