I can't come to any other conclusion than that commercial anti-discrimination laws infringe on the freedom of association. But so what? All laws infringe on some freedom. The question is, rather, do commercial anti-discrimination laws unjustly infringe on freedom of association? There are several reasons why they do not.
First, to engage in public commerce, a person necessarily waives some aspects of his or her freedom of association. If you have a business that is open to the public, you are saying that you wish to associate with the public at large. In a similar sense, if I leave my front door open (perhaps to show my house for sale), I am waiving my right to arbitrarily exclude people from entering it. A closed door is the signal that you may not enter without permission. This argument does not, of course, establish that there are no limits on waiving a right (leaving my front door open does not signal permission that people may take all my stuff), but if a person waives even a part of a right, then they have undermined the argument that the right is absolute. Once a person signals that they are intentionally waiving part of a right, it becomes a social construction, not purely an individual construction, as to precisely what parts of a right the person is waiving.
Even under theories of natural law, whenever we have a conflict of rights, then direct utilitarian concerns come to the fore. Since "natural law" is in conflict, we cannot use "natural law" to resolve the conflict. In the case of commercial anti-discrimination laws, we have a lot of evidence going back a century or more that discrimination causes more harm to the excluded than it does benefit to the excluding. This utilitarian conclusion depends on no small part on the truth that commerce, trade, and employment are not individually discretionary activities; instead, they are necessities of life. Permitting individually arbitrary discrimination risks excluding classes of people from the requirements of life, a considerable harm, but affords a benefit that is at best rarefied and abstract. The person denied the right to arbitrarily discriminate does not lose any economic necessity.
Finally, the legal resolution of the conflict between anti-discrimination and freedom of association is participatory, transparent, and deliberative. It is not being imposed by an unaccountable, exogenous source; it is instead being established by a government that is, to some extent, accountable to the people. Even the judiciary makes its decision-making process a matter of public record. The government is not just acting capriciously; there has been a process of public deliberation about how to resolve the conflict of rights.
If you admit to citizenship in a democracy, you (ideally) have the right to participate in the deliberation, but at some point you have to just say, "The people have spoken," and allow the judgement of the masses to override your own personal preferences. If you feel that individual preferences in some area should override the majority, then you can lobby for a constitutional right, and there are several avenues available: amend the US Constitution, amend your state constitution, or persuade the US Supreme Court or the state's constitutional court that your proposed right exists in the existing constitution.
The argument that the people should never override an individual's "conscience" is fundamentally anti-democratic. It affords sovereignty to the individual, not the people. There's nothing wrong a priori with individual sovereignty, but historically, we have abandoned the notion of a sovereign individual so long ago that reestablishing the notion would abandon millennia of political development and return us to... well, I'm not sure, perhaps a hunter-gatherer economy. Again, maybe not a bad idea, if we can keep seven billion people alive in such an economy. However, a return to individual sovereignty is a radical, revolutionary proposal; it therefore fails as an argument against a particular social construction in a democratic republic.