Humor me for a minute and allow me to make a significant number of generalizations and assumptions, most of which stem from my experience.
Theological liberals often tend to be political liberals as well. In this, they often want the State to act as an agent of compassion along with the Church. Political conservatives resist this on the grounds that it is not the State’s function or role. At the same time, theological liberals often want the State to remove itself from the business of marrying people, as this is the proper role of the Church.
Compare that to theological conservatives, who often happen to also be political conservatives. Typically, they wish to reduce the State’s role in acts of compassion as the State tends to be inept and such acts are the proper dominion of the Church. At the same time, they argue that the State has an interest in preserving traditional marriage.
I do not think the positions are actually internally contradictory. But framing them this way does expose the interesting tension between their understanding of the State’s role in society.