If the notion of the social construct is true, then the notion of the social construct is itself a social construct. It is without any basis in reality, so that there is no real reason we should notice it, or order our lives thereby.
The consequence is that when someone argues that, e.g., marriage is a social construct, so that we may change it if we like so that gays can marry, it can be argued with equivalent force that the notion that gays ought to be able to marry is likewise a social construct. We may therefore reject the notion of gay marriage, under the banner of social construction, and there will be no way that the moral nihilists can gainsay us. If there is no moral reality, so that no one has any basis in that reality for an argument against gay marriage, then by the same token no one has any basis in moral reality for an argument against the proscription of gay marriage – or anything else, whatsoever.
In general, it’s no good to argue from moral nominalism to any moral realism. You can’t get any ought from “there is no such thing really as an ought.” Thus to talk at all about what it is right or proper to do is implicitly to recognize the falsity of moral nominalism; if moral nominalism is true, then nothing is really right or wrong to do, and such talk is all just nonsense. Moral discourse of any sort at all implicitly agrees to the presupposition that moral discourse has something real to discuss.