If you own a business and you do business with ‘the public,’ this does not negate your Natural Rights, nor does it require you to subordinate those Natural Rights to government control. Anyone who claims otherwise is an enemy of liberty and seeks to control you — period!
‘Inalienable‘ means that your rights cannot be taken away or given up: they are an inherent aspect of your being. So, if I own a business and I do business with the public, I retain my Natural Right to Contract. The Natural Right to Contract means I willingly enter into an agreement with another person who willingly does the same with me. It does not mean I can be forced to enter into a contract with you simply because I am doing business with the public. That would be a contradiction to the definition of inalienable, and to do so is a violation of my Natural Right to refuse to do business with you. Anyone who claims otherwise is an enemy of liberty and seeks to control you.
Neither can we be forced to surrender our rights in return for permission to own and run a business. This is also a violation of Natural Law. First, government is the result of a contract between all citizens of a nation. Inherent in the Natural Right to Contract is the principle that the terms of that contract cannot demand the parties to the contract surrender that which they do not have the ability to surrender. Since your Natural Rights are inalienable, you cannot surrender them. Thus, the Social Contract can never demand that you surrender your rights. Anyone who claims otherwise is an enemy of liberty and seeks to control you.
The second reason you cannot be forced to surrender your rights in return for permission to operate your business is because you already have that right. You have a Natural Right to sustain your life, thus, you have a Natural Right to operate a business. In truth, the government violates the principles of Natural Law when it requires you to buy a business license. This is no different than forcing you to pay for the right to live, and it is a violation of your Natural Right to your life. Anyone who argues against these principles is an enemy of liberty and seeks to control you.
One last problem most people have with the notion that operating a public business means you surrender to government control is our understanding of what ‘public’ means. We have come to think of ‘public’ being equal to ‘government.’ We have also accepted the notion that the government is a person. Neither is true. ‘Public’ simply refers to the totality of private individuals. It has nothing to do with and exists totally outside of government. In fact, government is the creation of the public, and thus, the public is the master of government — not the other way around. Nor is government a person, therefore, it has no rights — only duties and responsibilities. This means government can never be the master or the public, and if it is no master of the public, then it has no authority to demand anything of us. Anyone who argues otherwise is an enemy of liberty and seeks to control you.
All of this is inherent in the Declaration of Independence and the principles of Natural Rights and Natural Law upon which it rests. Anyone who does not understand how and why this is true, that person does not understand the principles of liberty. And anyone who argues against these principles is an enemy of liberty who seeks to control you — period!
THE ROAD TO CONCORD 
Joe, How does this relate to the Civil Rights Act and the lunch counter sit-ins? Do you believe the act violated inalienable rights of those to contract? I believe this has been the stance of Sen. Rand Paul in the past; his view being the the free market would correct any issue that would arise.
I know that we have been taught otherwise, but YES! The ‘Civil Rights Act’ is a clear violation of Natural Law. The evidence is in the name. Placing ‘Civil” rights over my Natural Right is a violation of Natural Law — period.
The right to be a bigot is inherent in the right of conscience, and if you do not have the right to conscience, then you do not have free will. It is that simple.
That said, I agree: the market will eventually sort these things out — IF it is allowed to function. The problem is, we are prone to seek power, and this is a means of using peoples’ emotions to gain and wield that power. And, since we are also prone to being impatient, once that power has been seized, we want to use it as soon as possible. At that point, we have a hammer and everything starts to look like a nail that needs to be hammered flat.
NOTE: I say “we” because these are human flaws: inherent in our nature.