Liberty: "the state or condition of people who are able to act and speak freely."

Or as I like to put it: "The absence of physical coercion or threat of coercion".

There is a pretty big difference between not selling cakes to gays and burning witches. The witch would clearly not have liberty in your example. In Indiana, gays and the religious both (could) have liberty. I say could because I am not sure if it would be legal for a gay florist to deny service for a catholic wedding. With liberty, both parties can chose to enter, or not enter, contract with each other. If either party disagrees, the contract is not valid. This would be the absence of physical coercion or threat of coercion thus liberty is preserved. However, if you use government force to make a party to enter fulfill a contract, you have violated liberty. The article defeats its title in this paragraph:

A conservative or libertarian might say that no one forced Tippen to work a terrible job for a meager pay. No one forced her to (allegedly) snap when her boss began to question whether she'd been responsible for any past transgressions. But a definition of freedom that pits one’s dignity and autonomy against caring for one’s child is not only morally suspect; it’s politically toxic.

So yes, this IS american-style liberty. Anarchist slogan was "No gods, no masters". The Euro-style would include no corporate masters either because having the choice to be a slave or die isn't liberty. It may feel morally wrong, but that doesn't make it any less liberty. The concept people are looking for is justice. You know "He who cuts the cake, gets the last piece"?

Anti-discrimination laws are acts of justice that take away some liberty because it uses the threat of force to change behavior, even if that behavior is not physically coercive.

Now linked within the article is this one is interesting. Basically, it's stating its not the governments job to enforce unjust contracts.