I find it hard to believe people think God cares about this issue this much, given all the real sin in the world (ie social injustice and war) but anyway.There's a certain tendency to see sin as "really bad things that happen out there", while things that ordinary people we identify with want to do (especially if they involve sex) are seen as things that "God doesn't care about". Some of this is simply that we often care much more about thinking well of ourselves than of other people. Things we do, and things our friends do, are no big deal. Things done by far away people, things of a scale that we don't normally encounter, those we can safely label as sins without disturbing our own comfort.
But let's be honest, most of us here and now have suffered more because of the "little" sins that we inflict upon each other than due to war or huge societal injustices. It's only possible to imagine that God doesn't care about sex and the many ways that we hurt each other with it and because of it if we narrow our frame of reference down to only the person we choose to care about, the person who wants to do something which is a sin.
Few of us have started wars, but many of us have started rumors. I don't have the ability to wipe away social injustice, myself, today. But I do have the ability not to commit some petty injustice that would hurt one or two people.
And let's be honest. Sex, marriage, and relationships are one of the main areas of conflict that we as humans encounter. Sex and relationships are important to us. Why is it that so many movies and stories involve sex and relationships? Because drama is built on conflict and one of the main areas in which we have personal conflict is around our relationships.
So unless we believe that God doesn't care if we treat people well, unless we believe that he doesn't care whether or not we suffer: Yes, God does care about sex and marriage. He cares about it because one of the main ways that you personally can either make others happy or make their lives miserable is your treatment of your family and loved ones.