You have no understanding of the meaning of Liberty. I suggest you find some good sources and learn more about the topic. In fact, in the above you claim that a consumer's liberty is harmed by a business (property owner) that is willing to voluntarily enter an economic relationship. Yet, at the same time you fail to recognize the liberty of an unborn child and claim that it is paramount to a woman's liberty to murder another human being.
Your understanding of liberty could not be more incorrect.
Consumers have rights, business owners have rights. Here they appear to conflict and you insist on a legal resolution. Well, I've proposed one, that accommodates both. I laugh at your statement that I don't understand the meaning of liberty - your notion is your way or the highway, and if the consumer is tossed from your store because of your arbitrary (and secret) demand that he conform to your moral values, then tough toenails. I think you're a perfect candidate for progressivism.
As for abortion, that's off-topic for this thread. But I bet you're a male who'll never have to endure nine months of pregnancy with no support from family or partner. The woman's liberty and self-determination no doubt means nothing to you - and again, such callousness is more akin, IMO, to progressivism than conservatism.
I don't defend the horrible practice of abortion. But I defend a woman's liberty just as I do my own, and seek to deter and reduce abortions by other, more effective means than calling upon the police power of the state.