Ok, to start off, thank you for being logically consistent.

Now, I disagree with you. If you open a business to the public, you should be bound to serve any one who wishes to partake of your services. The only notable exceptions should not be related to any of the aforementioned criteria. Ie, you have to serve a black man, but if he is being a belligerent asshole, you're free to throw him out.

As to why, to begin with, you're not free. You only have the freedoms given to you by the society you live in. If you begin to allow businesses to discriminate based on intrinsic reasons (ie, religion, gender, ethnicity), then you are instituting a secondary class of citizens - those that cannot get their dry-cleaning done at certain places, stay in certain hotels, etc. The free market will not "fix" this problem, especially if those being marginalized are a small proportion of the population. If you have a good enough product, you can afford to be bigoted and turn away potential customers. Chick Fil'A is a good example of this. I'm sure there are people that won't eat there specifically because of their association to anti-gay groups (which I'm perfectly fine with that being legal, provided they don't turn away gay customers or job seekers). Even with the loss of potential customers, they're still doing quite fine because their product is just that good (or so I'm told; we don't have them here).

I'm all for the freedom for individuals to be racist assholes, and I certainly don't want to start jailing people for bigotry, but once you step into the public forum with a company, there are rules that you have to abide by. Currently those rules state you can't discriminate based on race or gender. I'd like to see sexuality added to that list.