I've been trying without success to follow the exchange between the SSPX and the CDF. 'What bee is in their bonnet now?' I ask myself.
Fortunately, we can rely on Jimmy Akin to break it all down for us in the most helpful way possible.
Here's a sample:
The L’OR author doesn’t spend a lot of time on the first two forms of assent, for these aren’t under discussion with the SSPX. Rather, it is assent of the third kind that is in question. On this subject, he says:
The Council’s other doctrinal teachings require of the faithful a degree of assent called “religious submission of will and intellect”. Precisely because it is “religious” assent, such assent is not based purely on rational motives. This kind of adherence does not take the form of an act of faith. Rather, it is an act of obedience that is not merely disciplinary, but is well-rooted in our confidence in the divine assistance given to the Magisterium, and therefore “within the logic of faith and under the impulse of obedience to the faith” (Congregation for the Doctrine of the Faith, Instruction Donum Veritatis, 24 May 1990, n. 23).This reflects the fact, discussed earlier, that the pastors of the Church are divinely guided even when they are not speaking infallibly.