One of the difficulties with standing on principle is that often one is defending them when they are practiced by bad people. Or when bad conduct is involved. In both kinds of cases one may have no sympathy at all for the specifics but still finds it important to defend the principle, as when one defends sleazy journalists or artists against those who would want to censor them.
In England recently a couple of homosexuals won a court case that forces bread and breakfast places to rent to them even when the owners disapprove of homosexuality. And, of course, the argument advanced was all about public accommodations, as if opening one's establishment for rent somehow committed one to accept every prospective renter. Why is that supposed to be a knock-down argument for forcing renters to rent to anyone? Presumably because commerce is a public action.
Now, by this line of reasoning censorship, too, should be allowed since most material that's the target of it is sold or viewed in public places or places that are adjacent to public places. This is how imposing government smoking regulations and bans on restaurants and bars is legally justified − these places all open onto public roads or sidewalks, so they are "affected with a public interest," a phrase first used in the USA by the Supreme Court in Munn v. Illinois (1877). Never mind that newspapers are often sold in kiosks and on street corners. But because of the explicit protection provided in the First Amendment to the US Constitution, they are immune to government regulation. (This may not hold as statute in the UK but is more of a tradition there, while it is indeed a constitutional principle in the USA.)
Whatever the law is, the moral fact of the matter is that one's sayings and writings may not be banned or regulated by anyone. Nor should one's decisions as to one's trading partners be subject to government regulation, however odious the terms are by which one accepts or rejects a trading partner.
Of course, in innumerable cases even if the government wants to regulate terms or trade it just cannot do so. One may decide not to purchase goods or services someplace because one knows that the owners are of a faith or political position that one opposes. Or they are of a race against which one is irrationally hostile. Millions of shoppers are free to engage in such unjust discrimination, while, of course, vendors are not (which, by the way, violates a cardinal feature of the rule of law, namely, that everyone is equal under the law − shoppers and vendors alike).
Conceivably, however, having announced in an advertisement that one's bed and breakfast place is available for rent does commit one to rent to any civilized person who comes up with the proper funds. Yes, that is a pretty good argument but in a free society it can be circumvented by making it clear, upfront, that one does not accept certain people as prospective renters. So if you place a notice to that effect in the advertisement or by the entrance, there ought to be no objection to excluding those whom you don't chose to deal with even if what you are doing is morally insidious.
The mere fact that one trades may not be used to subject parties to the trade to public micromanagement. After all, marriages are usually public − one must get a license − and so are many other noncommercial interactions with people. In a free society one must tolerate those who would deploy deplorable criteria for these as well as for doing business.
As much as it is a contemptible practice to reject homosexuals or blacks or whoever as prospective trading partners, it is even more contemptible to rob people of the liberty to determine whether they will do business with certain others. Yes, they need to be up front, otherwise by the standard of the reasonable person it is understood that anyone is welcome; yet if that is not one's choice, however insidious that may be, one who openly opts out ought not to be made to embrace it. Let neighbors, colleagues, family, friends and others exert peer pressure or boycotts so as to change such people's ways. But do not coerce them to do the right thing − it must be their free choice.
Unjustly discriminating against people isn't assault or battery or some other kind of aggression, so the law must not interfere with it.