""The idea that the church can have no influence or no involvement in the operation of the state is absolutely antithetical to the objectives and vision of our country,""
Santorum believe the church should have a role in the operation of the state.
How much more do you need?
Bill Buckley used to say, famously, that "whoever says A must also say B", but in this case, Santorum's A and your B are not quite the same, and are in fact different enough to generate quite a bit of daylight between Santorum's sequelae and yours.
He was referring to the fact that a grounding in Christian morals is essential to the operation of the American Republic -- our Framers said so repeatedly and warned us -- and the clergy -- that any great failure of public morals would lead to a failure of the Republic. We are seeing happen today what they feared even then.
Santorum said "no influence or no involvement": I do not think he wants prelates sitting in offices in the Executive Office Building or holding consistories in the cloakrooms of Congress. He is talking about the active efforts of the ACLU to expel theist Americans from every position of honor and profit under the United States, in order to promote scientific materialism, the official public religion of Stalinism.
He is criticizing and deploring the broad reach and influence of deeply hostile, anti-Christian NGO's in public life, as toxic to our freedom and the integrity of the Republic.