Only a few propositions apply to a Catholic State; nevertheless, all of the propositions are binding principles.
That statement is not correct. The idea of separation of Church and State is condemned, period, simply because the State has a moral duty to profess the true religion. This is clear from many encyclicals, for example Quas Primas of Pius XI, Libertas, of Leo XIII, VEHEMENTER NOS of Pius X, and many many more. Here’s just one:
Immortale Dei: "For, men living together in society are under the power of God no less than individuals are, and society, no less than individuals, owes gratitude to God who gave it being and maintains it and whose ever-bounteous goodness enriches it with countless blessings. Since, then, no one is allowed to be remiss in the service due to God, and since the chief duty of all men is to cling to religion in both its reaching and practice-not such religion as they may have a preference for, but the religion which God enjoins, and which certain and most clear marks show to be the only one true religion -it is a public crime to act as though there were no God. So, too, is it a sin for the State not to have care for religion as a something beyond its scope [this is what you always hear by Liberals today], or as of no practical benefit; or out of many forms of religion to adopt that one which chimes in with the fancy; for we are bound absolutely to worship God in that way which He has shown to be His will.
Now, it is true that a non-Catholic County is not going to submit to the Catholic Church, but that doesn’t mean that a non-Catholic Country is freed from the duty to do so by God.
It’s not likely to happen anytime soon in America, but that doesn’t mean it is good. In the same way, it is not likely that Americans would tolerate the forbidding of divorce and remarriage, but that does not make it right either. Unfortunately, America is a Masonic State, but we can always hold out hope that in the future it will be a truly Catholic State and recognize Jesus Christ as the King.
The Syllabus contains formally condemned errors, and it is just as binding today as it was 150 years ago. **If you disagree, please provide the magisterial document that rendered it null. **
Just because many people have embraced the errors today, does not mean the errors became true.