Practically speaking, using the hackneyed but real-world example of as bakery asked to supply a cake to celebrate a marriage between two people of the same sex, if this becomes law then legally a baker could refuse to engage in that commerce by declaring his participation would create tacit consent to an arrangement his religious beliefs about marriage find morally repugnant. This would occur regardless whether such marriages have legal recognition in the state.
As a result, the rejected party could try another vendor and the dissenter would lose business as a result. If the spurned really got upset, they could call for boycotts of the business and the like, which is their right in a free marketplace. They also could make the matter judicial by filing suit in state or federal court. But the state cannot do anything about it as a direct party.
Possibly indirectly, through its courts, the state could have an impact. Insofar as state law and the Constitution go, the rejected party could get no relief, as there is nothing in these that protects people from alleged discrimination on the basis of homosexual behavior (such protections are written into the Constitution for a number of immutable characteristics of people and for two other attitudinal/behavioral aspects, political and religious beliefs). However, it is possible that in limited circumstances that local ordinances that do extend nondiscrimination on the basis of sexual behavior preference could provide those parties relief, although it seems a stretch to envision a circumstance where belief about marriage would translate into an opportunity for refusal to perform a service in the subject matters that these cover.
Nor would resort to the federal judiciary likely provide relief, unless some major rewriting of the federal Constitution by judicial fiat occurs that would allow such intrusion into what the Constitution defines as a state power. While definitively contrary to the original intent within the document, history shows that level of disregard is possible, and certainly the impending Supreme Court decision on whether the Constitution should be redefined without amendment to give the federal government control over the definition of marriage could provide a chance for the considerable judicial activism necessary.
As another example of what the bill could do, assuming for the moment the Supreme Court rewrites the Constitution to prevent states from regulating marriage, the bill would permit an employer meeting its qualifications from treating for benefits purposes an employee having a married status if that union is claimed to be same-sex. But no one is putting a gun to the heads of people and forcing them to take certain jobs; just as in the example of a recalcitrant baker who turns down a request under the law, the disgruntled person can gain employment elsewhere if having an unrelated person of the same sex share in benefits is so important.
Note, however, the narrowness of the proposed law. For example, if a guy wants to have a cake made in honor of his loss of virginity through buggery, the law would not permit that kind of request to be turned down, because the activity in question has nothing to do with religious views on marriage.
Despite these facts, as naturally as the sun rises in the east the usual suspects have come out to complain about how the law discriminates on the basis of sexual preference, apparently ignorant about the First Amendment and/or eager to construct straw man arguments to create an environment where their moral views must be forced upon others by requiring these others to render tacit support of those views. Such intolerance and bigotry have no place in America, and it is regrettable that the state’s Democrats and some special interest groups have chosen to indulge in it.
The law’s importance, even with its limited reach, stems from requiring the state to remain neutral in religious views about marriage, where someone could be asked to violate those views by forcing their endorsement of acts contrary to those, and its disqualification to be utilized as an object of oppression of these individuals. Having to go to another vendor as a result of its application does not unduly inconvenience the class, defined by its members’ behavior, of people involved whose wishes are declined, and certainly not to the point where the First Amendment must be attenuated to satisfy that class. As such, it constitutes wise public policy that should become law.