Although it may not be acceptable to all in this situation, it would be acceptable to many. It is simply this: to obey the law and serve gay weddings, but to make it known publicly that you believe that the law forcing you to do this is unjust, needs to be changed, and is obeyed only under protest and out of your respect for law and the democratic process...
I could well imagine a pious religious couple, running the kind of wedding-focused catering hall that I once worked at in New York, posting on its premises an announcement something to this effect:
[lengthy statement declaring that the store owners are Christians, that they oppose "gay marriage and the "gay lifestyle," and that they will nevertheless provide the demanded services out of obedience to the law, but that they would like to see the law changed]
We are required by the Sexual Orientation and Gender Identity (SOGI) provision of New York State's anti-discrimination statute to make our wedding facilities available to anyone who seeks to use them, including gay and lesbian couples who want to marry under New York's same-sex marriage law. We believe strongly in the democratic process and the rule of law. For this reason, we will obey the state law governing our business. However, we obey this law only under the gravest protest, as we believe it violates our deepest moral and religious convictions. It does so needlessly and with apparent intent to polarize our country and inflame an already overheated cultural war.
Such a declaration would have many advantages over simply giving in silently to an unfair law to save one’s business. It would strike out in a public way against the injustice of such a law and gain sympathy from many quarters for the business owner’s point of view.
It would also cast the business owner in the sympathetic role of the admirable peacemaker. His opponents would be cast in the role of authoritarian bullies picking on pious religious folks and opposing simple live-and-let-live solutions to the problems posed by American pluralism. Finally, such a declaration would probably discourage gays and lesbians from ever wanting to hold their wedding celebrations at any establishment that posted such a statement. The catering hall owners would have a strong First Amendment right to air their views, and by doing so they would probably end most instances where they are asked to do what their religion and moral sense forbids.
It’s possible that such a declaration might drive away the business of liberals sympathetic to gay marriage, but it is just as likely that it would gain sympathy from many quarters, including not only from social conservatives who oppose gay marriage on principle, but from many liberals and moderates who resent small guys being pushed around by state bureaucrats. If the declaration were properly worded and sounded a courteous-yet-concerned tone of inclusiveness, it would probably attract and repel equal numbers of people. Most potential customers, I suspect, would not be affected one way or the other.
Suffice it to say that I am on the fence for this one. I think it is a good fallback position*, though I suppose that as a fallback position it loses some of the "we're just trying to leave in peace" overtones. I am also less-than convinced that it is a position that we will be allowed to fallback to--today, compulsion for participation, tomorrow laws against protesting against said compulsions. Today, it's free exercise of religion (and rights of association which are under assault--Constitutional protections thereof be damned--and tomorrow it will be the rights of free speech.
On the other hand, there is a slightly more aggressive version of this, in which the "shopkeepers" post (and state) that all proceeds from providing services to "gay marriages" (weddings, receptions, honeymoon,s etc as applicable) will go to support the National Organization for Marriage (or a comparable pro-marriage and frankly pro-sanity organization).
*Similarly, the idea that the Church should refer to the Sacrament only as "Holy Matrimony" and not ever as marriage," and to the civil institution/partnership as "marriage" but never matrimony, is a fallback position which ultimately leaves much to be desired. In both cases, there are better options even as "fallback" options.