> Liberalism as an ideology can be derived from two axioms

Those axioms don't really create a consistent or substantial ethical universe. If I'm a serial killer and I say, "don't worry, we're all moral equals. You're just as entitled to kill me as I am to kill you," then I'm not violating your first principle. And if you were to respond, "killing like that is simply wrong," you'd be violating your second principle and setting yourself up as a moral oracle.

The core of liberalism is not an underlying system of ethical axioms: Mill was both a liberal and a utilitarian, but you can just as easily argue against liberalism from a utilitarian standpoint—moreover, the position you're evincing here is liberal but anti-utilitarian. No, the unifying source of liberalism is the political status quo which produced it. The real champions of liberalism were the capital owners who stood to profit by it, and who had the influence to bring it about, ousting the aristocracy in the process. The idea that liberal hegemony is a moral triumph and not a political one is simply history being written by the victors.

> Liberalism is the ideology responsible for our prosperity.

It's more correct to say that liberalism and industrial prosperity were both products of the industrial revolution, rather than one being responsible for the other. Illiberal authoritarian powers like China and India are demonstrating that industrial prosperity is eminently attainable without liberalism, although I wouldn't consider that an endorsement of their respective ideologies.

> The first step on the path to evil is thinking you know better.

The first step to literally anything is thinking you know better. You can't escape the duty of having to make judgements. Inaction is itself an action that can cause harm, and there's no a priori reason to privilege the choice not to act.

> Raising hateful, illiterate children injures no one else.

It injures the children. Besides which, raising a sufficiently hateful child does injure others if you ultimately induce that child to commit a hate crime.

> Liberty consists in the freedom to do everything which injures no one else; hence the exercise of the natural rights of each man has no limits except those which assure to the other members of the society the enjoyment of the same rights. - Declaration of the Rights of Man - 1789

The operant question here is what it means to "injure someone else" and how we intend to "limit the rights of other men to assure others' enjoyment of the same rights." Natural rights are a very flexible concept. Do I have a right to healthcare, or do hospitals have a right to deny me care for profit? Do I have a right to dump my garbage in the river, or do you have a right to clean drinking water? "Natural" rights are an oxymoron; every right is contrived, and deciding which rights we choose to legitimize and prioritize allows us to sculpt a flavour of natural rights theory to suit any belief system whatsoever. For example, just about anyone would agree that a person has a right to evict a violent burglar from their home. A conservative might further argue that Americans have a right to violently detain illegal immigrants in defence of their borders. Finally, a Nazi might plead that Aryans have an absolute right to defend their homeland from ethnic invaders. By tweaking exactly which rights you get and to what extent you get them, you can justify practically anything. That's why I find utilitarianism so much more rigorous.