Is Austrian Economics value free? Is Mainstream Economics value-free? Why or why not?
Economics qua economics is value free, as a rule.
But seeing as the innate utilitarianism in our minds generally takes general prosperity as good, which means that Austrian economics tend to have implicit values.
The difference between libertarianism and socialism is that libertarians will tolerate the existence of a socialist community, but socialists can't tolerate a libertarian community.
All economics is value-free, by definition. If an Austrian or a mainstreamer discuss values, there's nothing wrong with that (in fact it's crucial), but they do so as moral/political philosophers, not economists.
That being said, Austrians tend to be natural rights libertarians who see that even if one were a utilitarian, one should pursue liberty. Mainstreamers tend to be utilitarians who sneak in their moral philosophy under a "scientific" and "value-free" fog.
Austrian Theory of the Business Cycle in 9 steps (Soliciting comments)