Any Christian who believes this doesn't truly understand the very nature of Christianity. When He walked on this earth, Jesus Christ very clearly stated that His followers could expect to be persecuted, and that the basic premise of Christianity was that these followers would always be seeking the "narrow gate." As such, we should approach the world with the expectation that the culture in which we live will reject everything we stand for.
You want to know how to strengthen marriage among Christians? Have the government outlaw it entirely.
Judging me on my understanding of Christianity, are you?
While Jesus did intend to change the hearts of His Disciples, He also required them to do good works. Allowing our culture to slip into a sewer without any attempt to engage it is akin to allowing the hungry to starve or the naked to freeze.
The fallen world has rejected heaven. Heaven has not rejected the fallen world. It thrust itself into the world mightily with the Incarnation. G-d has not given up on it yet. We are called to advance heaven while we draw breath. We do so heart by heart, and also by establishing righteousness where we can.
Shalom.
But individual actions do have an effect on larger institutions and on society as a whole. If you want to do good, that may involve taking an interest in what happens to the institutions, including government, that protect order.
This seems to be the way things work: Christians do generally withdraw from public life, until the point comes when things get so muddled, that they reenter the public and political spheres in the hopes of making sense of things, saving what can be saved, and doing some good. Hopefully they act in time. Eventually political action doesn't fulfill the hopes they have, and they retreat again.
This may not be the right issue or the right time to get activist. But Christians have gotten involved in politics in the past, and when the stakes are high, will do so again in the future.
Your point about persecution is good, but the rest of your point doesn't follow. If we shouldn't bother trying to get society to do marriage right, then we shouldn't have bothered getting society to end slavery or Jim Crow.