If such a line exists at all, it does not run through a church. The Catholic Church, as is any church, is free to conduct its business as it sees fit, so long as the rights of others are respected. What part of "free exercise" does the author not understand?
"Where is the line that separates church and state?"
The separation of Church and State means that the government will not finance a Church or regulate a Church. I don't see the GOP granting financial favoritism to any religion or sect.
Will someone explain to me how school prayer, God in the national pledge, and a (we can hope, right?) ban on pre-natal infanticide are violations of that separation?