With regards to the quote from the “G8” Cardinal, I don’t think he’s referring to the theological modernism condemned in Pascendi. Given the context of his relating it to the decisions of the First Vaitcan Council and to reactions against injustice and abuses against human diginity and rights, as well as later affirming an objective standard that the Church must always conform itself to, it doesn’t seem like he is referring to the theological modernism of Loisy, etc, but rather aspects of civil Liberalism or “modern society.”
Especially in light of his criticism of secularism and laicism in Europe and elsewhere today in that speech, it seems more like a less sophisticated attempt to reiterate what Joseph Ratzinger wrote on this topic in “Principles of Catholic Theology” with regard to the Church’s relationship to various forms of moderated Liberalism and modernity. I don’t think that he is claiming that Vatican II embraced rationalism or theological modernism (ie that there is no objective source of revelation or that it exists, but should not play a role in society). Rather, Vatican II moved the Church’s orientation toward modern society as that of engagement rather than antagonism.
As I mentioned, Liberalism had become moderated from it’s anti-clerical and anti-Catholic status in the 19th century and after WWII seemed to be a system the Church could now work within, promoting what was good and purifying what was not, rather than reject it outright as was necessary in the century prior.
Of course, a lot of the things that caused the Church to outright condemn it in the 19th century are gaining momentum again.