Of course it is a privilege. What planet are you from?
Rights are things that exist in and of themselves and do not burden any other individual, nor are they conferred by government. They are that which "nature and nature's God" entitle human beings. You have an inherent right to free speech, for example, but not a right to be listened to because that would burden others.
Marriage is, as gay activists define it, public recognition of a relationship with attendant social and government benefits. That is not a private matter and burdens other people. Thus, a privilege.
If gays want to "marry" in a liberal church, fine -- as long as it does not come with government recognition and benefits.