Left versus right is a horrible way to frame political dialog because there really aren't good definitions for either.

All of your points center on taxation. Taxation alone doesn't make one an authoritarian. Libertarianism is an umbrella of ideologies which includes classical liberalism; an ideology that fundamentally recognizes the necessity of the state in organizing the societies of men, while also recognizing its destructive potential and seeking to limit it. The objective reality is that the world is organized into states. The state has proven to be the most effective form of government in staving off outside threats to a political society. As libertarians, we all recognize the faults of the state and seek to limit its authority, to keep the political power of the state divided, and to generally have political power retained by the individual.

You mention different types of welfare. There used to exist mutual aid societies in the US. When the Great Depression hit, any nobody had work, the funds of these societies ran dry rather quick. With the programs of the New Deal, those societies never rebuilt. With the general, consistent economic prosperity of the post-World War II United States, maybe that model could have worked barring the recession of the 1970s and of course the Great Recession.

The less government you want, the more libertarian you are. I don't entirely agree with this. If I want government to enforce property rights, I'm less libertarian than the person that doesn't want government or property rights? If I want government to enforce the individual right to liberty, I'm less libertarian than the person practicing chattel slavery?

Moving back to the compass itself, the compass test when I last took it doesn't distinguish between a person answering a question about how society should look, and whether that person thinks it is the role of government to enforce that view upon society. So an individual can be religious, and the compass puts them on the right. A person can think that worker cooperatives are more just than the modern shareholder corporation, and the compass puts them on the left. Libertarianism versus authoritarianism is about the use of force by the state, not what somebody thinks an ideal society looks like.