The problem with the supposed quotes from the Syllabus of Errors is that they are obviously not direct quotes, because if they were these quotes would be condemned by the syllabus as error.
In reality, the quotes submitted were distortions of what is actually being said, and considering the extremely precise language that is used in such documents, a summary from a third party simply won't do.
For instance, if I say...
[it is error that...] Protestants alone should be allowed to be the President of the United States.
...for someone to reformulate that into a positive statement which says...
"It is a requirement that a Catholic HAS to be the President of the United States."
...would be erronious. That's not what I said at all, I'm simply saying that it should be left open as an option for a Catholic to be president, a Catholic should not be barred from the presidency by virtue of his profession of faith. (Same goes for a Protestant.)
That is what a lot of the actual quotes are saying, that certain Catholic ideas shouldn't be condemned outright (referring to local European philosophies of that time period which often ran counter to Catholicism and Christianity in general), not that it is a requirement that they be implemented worldwide. I know it's shocking to Americans to even dream of a government different than their own that could actually somewhat work, but for a lot of history many states were tied up with the majority religion, and there are of course pros and cons to that, just as there are pros and cons to democracy. For instance, in a Catholic state abortion would never have been made legal. That doesn't mean there has to be a theocracy and that everyone would be forced to be Catholic, it just means the laws were based on Christian Catholic concepts and Catholicism was the way of the land. The document is saying the idea that this kind of government should be outright condemned and that it could never work is erronious. It's not saying Catholics need to take over the world and enforce that kind of government everywhere. But if people got together and decided that's what kind of government they wanted, they shouldn't be stopped from doing that.
Anyway, there is a very interesting article here
that goes through the syllabus line by line and explains what was meant, and what wasn't meant. Here are some excerpts:
Many of the errors condemned in this section [referring to section IV] were from a time when the popes were both Supreme Pontiffs of the universal church and also temporal princes in their own rights. (Bl. Pope Pius IX was the last pope who was also a temporal prince.) The Italian army seized the Papal States in 1870 and the popes were basically confined to the Vatican until 1929 when the independent Vatican City state was created by the Lateran Treaty of 1929. (Based on a Concordant between the Holy See and the Italian government under Benito Mussolini.) Because of these circumstances, many of these errors are not applicable today as they were when they were issued due to the changed political landscape. This is a significant nuance that is often not taken into account by detractors to the Magisterium...
[it is error that...]24. The Church has not the power of using force, nor has she any temporal power, direct or indirect. -- Apostolic Letter "Ad Apostolicae," Aug. 22, 1851.
[it is error that...]25. Besides the power inherent in the episcopate, other temporal power has been attributed to it by the civil authority granted either explicitly or tacitly, which on that account is revocable by the civil authority whenever it thinks fit. -- Ibid.
Since 1870, this condemnation is no longer applicable. Vatican City has no army and the Swiss Guard are hardly invasion-force material to put it bluntly. Since Vatican City is a sovereign state, there is some temporal power, however limited. Thus by example all popes since 1929 have exercised some temporal power, and that is adequate to refute the assertion that the Church has no temporal power. As for point twenty-five, Vatican II taught that the episcopate was invested with power from God, not temporal governments. Also, at no time has the Church taught that she has no right to possess temporal power. The Papal States were seized by Italy in 1870 and the popes since that time have had to live with that fact. By no means does this accommodation imply granting assent to condemned proposition twenty-five though.
[it is error that...]55. The Church ought to be separated from the State, and the State from the Church. -- Allocution "Acerbissimum," Sept. 27, 1852. In 1864, Pius IX had issued his Syllabus of Errors. Among the condemned propositions was that "the church should be separated from the state and the state from the church." Archbishop Spalding of Baltimore issued a pastoral letter stating that the pope "evidently intended" his words "for the stand-point of European radicals and infidels," who sought to undermine the Church. Far different, he argued, was the First Amendment that laid "down the sound and equitable principle that civil government, adhering strictly to its own appropriate sphere of political duty, pledged itself not to interfere with religious matters, which it rightly viewed as entirely without the bounds of its competency."
Archbishop Spaulding received no rebuke from Rome for his interpretation of point fifty-five of the Syllabus where he pointed out that the target of the condemnation was "European radicals and infidels who sought to undermine the Church." It therefore cannot be taken in and of itself as a condemnation of the sort of separation that a constitutional republic would make between church and state.
[it is error that...]77. In the present day it is no longer expedient that the Catholic religion should be held as the only religion of the State, to the exclusion of all other forms of worship. -- Allocution "Nemo vestrum," July 26, 1855.
The explanation of the great theologian Ven. John Henry Cardinal Newman from his Letter to the Duke of Norfolk
will be referenced as Newman spoke on this theme: When we turn to the Allocution, which is the ground of its being put into the Syllabus, what do we find there? First, that the Pope was speaking, not of States universally, but of one particular State, Spain, definitely Spain; secondly, that he was not noting the erroneous proposition directly, or categorically, but was protesting against the breach in many ways of the Concordat on the part of the Spanish government; further, that he was NOT referring to any work containing the said proposition, NOR contemplating any proposition at all; NOR, on the other hand, using any word of condemnation whatever, NOR using any harsher terms of the Government in question than an expression of "his wonder and distress". And again, taking the Pope's remonstrance as it stands, is it any great cause of complaint to Englishmen, who so lately were severe in their legislation upon Unitarians, Catholics, unbelievers, and others, that the Pope merely does not think it expedient for every state from this time forth to tolerate every sort of religion on its territory, and to disestablish the Church at once? For this is all that he denies.
[it is error that...]78. Hence it has been wisely decided by law, in some Catholic countries, that persons coming to reside therein shall enjoy the public exercise of their own peculiar worship. -- Allocution "Acerbissimum," Sept. 27, 1852.
This...is an injunction against the civil authority of a Catholic
nation. The error is presuming that in a Catholic country it is wise to promulgate civil laws to declare the non-Catholic to have public exercise of their religion. [my note - seeing as we don't really have any Catholic countries around anymore, the point is quite moot. Likewise, that does not mean there could not be freedom of religion, just that it would not be necessary to make civil laws concerning other religions.
] Vatican II, with the subject of religious liberty, dealt with the rights of individuals to freedom from coersion from practicing their religion provided that they were not disturbing the public order. Here is how public order was defined by Dignitatis Humanae
: The right to religious freedom is exercised in human society: hence its exercise is subject to certain regulatory norms. In the use of all freedoms the moral principle of personal and social responsibility is to be observed. In the exercise of their rights, individual men and social groups are bound by the moral law to have respect both for the rights of others and for their own duties toward others and for the common welfare of all. Men are to deal with their fellows in justice and civility.
Furthermore, society has the right to defend itself against possible abuses committed on the pretext of freedom of religion. It is the special duty of government to provide this protection. However, government is not to act in an arbitrary fashion or in an unfair spirit of partisanship. Its action is to be controlled by juridical norms which are in conformity with the objective moral order. These norms arise out of the need for the effective safeguard of the rights of all citizens and for the peaceful settlement of conflicts of rights, also out of the need for an adequate care of genuine public peace, which comes about when men live together in good order and in true justice, and finally out of the need for a proper guardianship of public morality.
These matters constitute the basic component of the common welfare: they are what is meant by public order.
Anyway, the whole thing has lots of good info if anyone is interested, I've got laundry to do!