The doctrine of the Church also recognizes implicit baptism of desire.  This consists in doing the will of God. God knows all men and He knows that amongst Protestants, Muslims, Buddhists and in the whole of humanity there are men of good will. They receive the grace of baptism without knowing it, but in an effective way. In this way they become part of the Church.

The error consists in thinking that they are saved by their religion.  They are saved in their religion but not by it. There is no Buddhist church in heaven, no Protestant church. This is perhaps hard to accept, but it is the truth. I did not found the Church, but rather Our Lord the Son of God.  As priests we must state the truth.

https://www.sspxasia.com/Docuмents/Archbishop-Lefebvre/OpenLetterToConfusedCatholics/Chapter-10.htm

DZ 1716 - In the worship of any religion whatever, men can find the way to eternal salvation, and can attain eternal salvation.

Leaving aside whether Pius IX and Lefebvre can be reconciled here, is Pius IX's statements in Syllabus of Errors ex cathedra?

The binding power of the Syllabus of Pius IX is differently explained by Catholic theologians. All are of the opinion that many of the propositions are condemned if not in the Syllabus, then certainly in other final decisions of the infallible teaching authority of the Church, for instance in the Encyclical "Quanta Cura". There is no agreement, however, on the question whether each thesis condemned in the Syllabus is infallibly false, merely because it is condemned in the Syllabus. Many theologians are of the opinion that to the Syllabus as such an infallible teaching authority is to be ascribed, whether due to an ex-cathedra decision by the pope or to the subsequent acceptance by the Church. Others question this. So long as Rome has not decided the question, everyone is free to follow the opinion he chooses. Even should the condemnation of many propositions not possess that unchangeableness peculiar to infallible decisions, nevertheless the binding force of the condemnation in regard to all the propositions is beyond doubt. For the Syllabus, as appears from the official communication of Cardinal Antonelli, is a decision given by the pope speaking as universal teacher and judge to Catholics the world over. All Catholics, therefore, are bound to accept the Syllabus. Exteriorly they may neither in word nor in writing oppose its contents; they must also assent to it interiorly.

http://www.newadvent.org/cathen/14368b.htm

Whether or not strictly infallible, they're clearly binding on Catholics.

If one keeps questioning the authority of this kind of teaching, then why isn't it OK to be a Modernist, since Modernism was not condemned infallibly either?  Where does it end?  This narrow view of infallibility would turn the Church into the free-for-all that the Conciliar establishment is.

Do we Traditional Catholics just happen to all agree with St. Pius X's condemnation of Modernism?  Is that all there is to it?

Yes, tragically, Archbishop Lefebvre had been misled on this subject.  EENS does not mean no salvation except by means of the Church, but, rather, no salvation except IN the Church.  Now +Lefebvre claims that by this invisible Baptism of Desire they are, unbeknownst to themselves, in the Church.  How is this a lick different from Karl Rathner's Anonymous Christian theology?

Its arguments like these that make me very sympathetic to the "Vatican II is reconcilable, but the way it was applied was a total mess" response to the crisis.

Oh, indeed.  I have repeatedly said that if I believed in the ecclesiology held by most Traditonal Catholics, I would without a question hold Vatican II as clearly reconcilable with Tradition ... even if many of its statements were inopportune given the climate they were made in.

Yes, but even that follows logically from the new ecclesiology.

People have a right to please God and to save their souls.  If people please God and save their souls by following their even-erroneous consciences, then they have a right to follow their even-erroneous consciences.  Once you subjectivize salvation, then Religious Liberty simply follows as a logical consequence.  If a Prot saves his soul by following his false heretical beliefs, then I could actually be interfering with his salvation by trying to pressure hi to abandon and compromise those things which he believes are necessary for salvation.

Well with +Lefebvre at least, the word "by" would be false.  It would be more like "despite."