First time commenter here so take it easy lol.
But in regards to EENS and what we typically think in regards to BOD a couple distinctions should be made. First and foremost if we are gonna compare Catholic and V2 Ecclisiology we have to do it honestly and actually show what they say.
Catholic teaching= only the Catholic religion/Church is salvific.
V2= the Holy Ghost uses other religions as a means of salvation.
So for people to rip on Trad priests claiming they believe the same thing is just not true. If you have a problem with them using phrases like "in spite of paganism " or when they refer to people saved "in false religions" its obviously clear they do not mean the above V2 Ecclisiology as demonstrated by other supporting comments. If you think it's wrong to say that, that's your opinion, but to characterize them the same as modernists is dishonest when they follow the Thomistic theology of approved theologians to get those conclusions.
Now to me it seems people get so hung up on phrases like these they dont understand that fact that a BOD recipient would not be properly speaking, in the visible Church Militant, because by necessity they have died. So they are not saying some random Hindu in India is part of the Church, what they are saying is if such a person, is actually in Invincible ignorance, follows the prescribed conditions as laid out by Pius IX and his contemporaries, such a person COULD be saved by a rare miracle before they die, being converted to the Faith. Now as to how much they must explicitly know has been debated by theologians and the popular opinion is that the Trinity, Incarnation and faith in Christ is a must, so following the principles of the approved teachings on BOD and Invincible ignorance it stands to reason God would enlighten such a person. So they die as Catholics not pagans, that is not the same as V2 which says the HINDU RELIGION in and of itself can be salvific. Thanks for reading.