15. Every man is free to embrace and profess that religion which, guided by the light of reason, he shall consider true. -- Allocution "Maxima quidem," June 9, 1862; Damnatio "Multiplices inter," June 10, 1851.
16. Man may, in the observance of any religion whatever, find the way of eternal salvation, and arrive at eternal salvation. -- Encyclical "Qui pluribus," Nov. 9, 1846.
17. Good hope at least is to be entertained of the eternal salvation of all those who are not at all in the true Church of Christ. -- Encyclical "Quanto conficiamur," Aug. 10, 1863, etc.
Sounds like Father Barron would disagree with Pius IX on all of these errors. But then again, these condemnations were pre-Vatican II; it's come to my attention here and other places that "things have changed". They sure have: that's the problem.
"...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..."