John F. Fink, former OSV president and publisher, wrote about Archbishop Noll's views on this and related matters in his book "Patriotic Leaders of the Church" Here is an excerpt:
In the process of defending the Church against the forces of anti-Catholicism, Bishop Noll wrote often about the separation of church and state. He ... emphasized the difference between this separation in the United States and that practiced in some European countries:
In the United States, not only is perfect freedom granted to all religions to carry on their work without interference from the State, but the Church’s religious activities are actively encouraged by the State. This sort of separation of Church and State has always been quite satisfactory to the Catholic Church, which demands only liberty to execute her divine mission. But in European countries separation of Church and State has almost invariably meant a great curtailment of religious activities after the confiscation of property of the Church and the closing of its schools.
When discussing this subject, the bishop always asked for the meaning of the words “separation of church and state.” “Do you understand it in the American sense of ‘a free church in a free state,’ or in the European sense of ‘an enslaved church in an anti-religious state’?” He was, however, also quick to point out that the Catholic Church does not believe in absolute separation of church and state:
The Church’s clear teaching is that there should be cooperation rather than antagonism between the state and church because both deal with the same citizens, one in relation to his eternal interests and the other in relation to his temporal interests. Where practically all the people of a nation are also members of the one Church, under the democratic principle that the people rule, there certainly should not be a complete separation of church and state, especially not such separation as enemies of the Church demand, which consists in the subjugation of the church, divinely commissioned to promote religion and morality, to the state. Where is the recognition of people’s inalienable rights to liberty or religious practice and the pursuit of eternal happiness under such conditions?
... Although he did not want a union of church and state in the United States, Bishop Noll wrote and spoke vigorously against those who promoted the “separation of religious influence from the lives of the people and the nation.” He felt strongly that America could be strong only when its citizens obeyed moral principles. “Genuine citizenship is based on justice,” he wrote, “as is also a sound social and economic order, but there can be no justice without religion."
Read the entire chapter on Archbishop Noll.