This would be a major retreat for the Church. As Catholics we believe it to be our obligation to inform the civil society in matters of public good. It is not enough to limit our opposition to practicing Catholics, just like we don't limit our opposition to abortion to just Catholics. Fully secular homosexual quasi-marriage is still a horrible idea that must be opposed on all levels.
Besides, it is not as easy as it sounds. The Church holds all apparent marriages to be valid till proven otherwise. For example, if a Jew marries a Muslim, and then both convert to Catholicism, their priest might recommend that they celebrate a sacramental marriage, but it will not be like they were not married before. If for some reason they do not repeat their vows in the Church, and instead at some point seek annulment, the Church will presume them a Jew and a Muslim to be validly married before God. In fact, it would be harder for them to obtain an annulment precisely because, as a Jew and a Muslim at the time their marriage was initiated, they were free to follow their own ceremony, and so nothing damaging to their marriage can be found in how it was solemnized.
That is a fanciful example to make a point. More commonly, two indifferent to religion people marry and divorce and then one of them or both become Catholic, and all of a sudden that frivolous marriage back in the day becomes a marriage not before justice of the peace but before God, and they need an annulment. That annulment will not be granted simply because it was secular, the Church must find a defect in the inception of it according to their religious affiliation, or lack of it, at the time.
So fast forward to the brave new world of secumarriage (whatever that thing is) unrelated to the Church marriage. If secumarriage is of the same sex, it is clearly not a marriage, end of story. But what of a man and a woman, both free to marry (not married before, neither a monk, a priest or a nun, etc.) intending to marry for life, in fidelity, desiring children, and getting secumarried? What is their marital status before God? Today, it is that they are married unless proven otherwise. Tomorrow -- we don't know. But we must know what the guiding principles will be. If one of them or both become Catholic, this is not an academic question.
The mechanics of marriage are really quite simple and actually pretty much universal the world over. As a civil ceremony, it can be whatever the State decides it should be. As a God ordained sacrament it has much more clearly defined parameters. In the past, marriage the civil ceremony was conducted in Churches in combination with marriage the religious ceremony, as the conditions for marriage were pretty much the same, and the bits the State insisted on (eg signing books for government records) were not a problem for the church. Now, if governments the world over, pressured by the gay lobby, decide to change the very definition of what marriage is, there is going to be a falling out. They can define marriage however they like, in the same way that they can call a dog a cat, but likewise, it is not truly what real marriage is, in the same way that the dog is never going say "miaow".