Marriage is not about elevating any given identity group rights over any other. Anywhere you look on the globe, any culture, at any point in history, no matter the veriation it takes marriage is about the raising and socializing of children; therefore any couple raising and socializing children should have access to it, while no couple who is not raising and socializing children should be permitted.
While your opinion is your own, I disagree with this part of your statement. Marriage is not simply about the raising and socialization of children. It's a form of social insurance, too, when you think about it. One of the problems in society is how to care for an individual when they can no longer care for themselves. If single, an individual with Alzheimer’s or cancer might be fortunate enough to rely on friends or family. But then again, they might not, in which case they will fall under the responsibility of the state -- often at substantial cost. The benefit of a marital partner, for both the individual and society, is to help guarantee that one will not have to rely on the government during times of need. From a purely economic perspective, marriage serves as a form of social insurance. You know the old vow "for richer or poorer, in sickness and health", and for this reason elderly and sterile couples are permitted -- even encouraged -- to marry, not because they will bear children, but rather because marriage promotes individual and societal stability.
Of course marriage is more than just social insurance. It's an expression of love, too. When people decide to wed, it's not usually because they are contemplating the insurance features of marriage, but rather because they are in love and want to make a binding commitment to be together for life. Marriage is not just about procreation and child-rearing. It's a system of insurance and a guarantee of stability, an expression of love and a promise of lifelong companionship. So no, "at any point in history", this is not true, because recent history demonstrates marriage is a more expanded institution besides a vehicle for simply raising kids under the best circumstances.
As an aside, I found your quote, that
"Only Liberals view politics through the eyes of categorizing everyone into identity groups" to be nothing but an off-base generalization at best. Conservatives, too, are certainly guilty of such a thing - "America is a christian nation", for example, as well as "democrats are socialists", and the very topic dealt with in this thread, "marriage is between a man and a woman". To claim that one political belief is categorizing people into identity groups while failing to acknowledge the reality that the other does the same thing is simply being partisan.