Marriage was a religious institution before it was an institution of the USA. The state doesn't regulate services or how we get married or who marries us, just the actual union and its benefits. Marriage can just be removed from the state allowing churches to do by at they want with marrying, and civil unions could be made as the replacement for all marriages declared under the state so we still have the same system but a different idea behind it. Does that sound reasonable enough?
The concept of marriage was never a religious institution to begin with. Many people don't seem to realize that marriage existed before every known major religion in the world and was practiced in every known civilization throughout human history. Many same-sex couples were married in ancient Mesopotamia, as well as several Native American tribes. The concept of marriage changes rapidly for many different reasons as society progresses whereas religion does not really change at all.
Marriage was never exclusive to any particular religion. And if it was, that means we would have to decide which of the millions of religions marriage belongs to. Atheists and non-religious groups would also not be allowed to marry, not just homosexuals. That would be biased discrimination.
If you go back to the oldest civilizations Mesopotamia, Egypt, Greece, Rome, there was still marriage. Only it wasn't the marriage you know of. Marriage back then was considered a treaty or business, for two family's. That's where arranged marriages come from (which was the original process how a wedding was carried out) only when religion started getting involved with marriage it became associated with love, wedding rings etc. Before that polygamy was allot more common than it is now. A woman became her husbands possession although it was his job to provide she could never step out of line. Cooking, sex and cleaning was the schedule for woman who were married back then. So really marriage has nothing to do with religion. It was just adopted by religion.
Has religion done enough in certain categories, marriage shouldn't be one of them, marriage has instigated entire cultures, obviously beliefs, conflicts. There are many thing religion has categorized, lifestyles is one, work labor too, voting rights, citizenship, immigration policies, and politics as well. We've let religion do enough, let's not let religion interfere with the matrimony of two people.