A private business being private property, one could make the same erroneous argument about any form of property. For example, I'm sure you would agree that there is no conflict between the idea of a home owner having final decision over who he does and doesn't allow into his home, and the fact that that home owner still enjoys police protection of his property. The right to own property does not imply that the property owner should be forced to dispose of that property in a way he doesn't see fit. Nor does the refusal to provide service to a particular person infringe upon that person's rights, unless you believe that said person has the right to enslave an unwilling person to his or her needs.
Furthermore, the fact that a business owner might complain about taxation does in no way imply that such a person resents paying for the services that his business benefits from - all it means is that they resent paying over the odds in order to fund things that they don't use or benefit from. And to preempt a potential retort, that in turn does not imply that such a person is mean, or uncharitable, since it has been shown that people who believe in individual responsibility or limited government give more to charity, donate more blood and do more voluntary work.
None of that follows through at all. Nothing above implies in the slightest that individual freedom is "just about wealth." It does however imply that the freedom to dispose of one's wealth as one sees fit is an essential part of freedom. The freedom to own and dispose of wealth does not abrogate anyone else's freedom. Also, the freedom to buy property does not mean the freedom to decide who can go where, except within the boundaries of that property. If you have ever owned a home, you will have no trouble understanding this.
I guess people who base their entire existence on the opinion that others are responsible for providing their needs would find the concept of individual responsibility, aka "freedom," very repressive indeed, yes.
This is so off the mark it's unreal. Where, in anything I said, did I imply that the protection of minorities is something that means protecting their right to do anything they like? This straw man argument suggests to me that like many who find the idea of libertarianism frightening, you're simply confusing libertarianism with anarchy. Libertarianism is based on the not-so-frightening principle that an individual is free to live his life in the way he chooses, so long as it doesn't interfere with the right of someone else to do the same. So an individual has the right to drive a car, but he doesn't have the right to drive it in such a way that he risks the lives of others. Likewise for pedestrians. The wider issue is that if roads were privately owned, then it becomes an issue of property owners deciding the rules which apply on their property.
Please quote the part of my post where I talked about having no government at all. Seriously, as many libertarians will tell you, arguing the case is a very tedious affair indeed when the person who disagrees with you resorts to simply lying about what you have and haven't said. I get this all the time: I will promote the idea of "limited government" and then someone will respond with "you support no government? That's just anarchy!!" I note that the Tea Party movement has to contend with the same straw man argument, that they are "anti government" instead of "pro smaller government." But whatever.