Yes, it is a good argument. And I can certainly see the reasons for the churches to break from the state.
At the same time, if civil marriages become the norm for the secualar world, then gays would indeed have full equality, and there is something to be said for fighting full equality for moral and social reasons.
In this sense, it would be ideal to make gays stop at civil unions, and continue defining marriage as one man/one woman.
The problem with the state’s involvement, at least in the modern era, is that the definition it uses to recognize the institution is simply whatever judges, pols or the majority thinks it is at any one time. And that’s it.
“Now, since the family and human society at large spring from marriage, these men will on no account allow matrimony to be the subject of the jurisdiction of the Church. Nay, they endeavor to deprive it of all holiness, and so bring it within the contracted sphere of those rights which, having been instituted by man, are ruled and administered by the civil jurisprudence of the community. Wherefore it necessarily follows that they attribute all power over marriage to civil rulers, and allow none whatever to the Church; and, when the Church exercises any such power, they think that she acts either by favor of the civil authority or to its injury. Now is the time, they say, for the heads of the State to vindicate their rights unflinchingly, and to do their best to settle all that relates to marriage according as to them seems good.”
—Pope Leo XIII about 130 years ago.
Freegards