This is why it is simply not a mortal sin to believe it, not that it has ever been confirmed. The point of the doctrine is not to enforce the idea that non-Catholics can go to Heaven, just that we cannot be sure of the state of the souls of all unbaptized (even if the probability of their salvation is near zero). The point is to leave it up to Mystery, like oh so many other things in doctrine.
Just because someone isn't a Feeney-ite does not mean they believe the exact, polar opposite of what Fr. Feeney argued either. That is presumptuous at the very least. It would be like saying because I don't believe Mary was immaculate conceived means I don't believe Mary was ever virgin either. And only the Protestants have that kind of thinking. The Eastern Orthodox certainly believe she was ever-virgin. Very few theological issues are necessarily on clear two part distinct positions.
Fr. Feeney was right to preach against ecumenism. But so do the SSPX, and they are not Feeney-ites. All Catholics agree that there is not salvation outside the Church. But the disagreement is whether someone can enter the Church without physically and visibly receiving the sacrament of baptism. One side argues that God never bound Himself to such things, the other retorts to say if that is the case, than can't people be miraculously baptized?
Invincible Ignorance is the idea that coming across a native never exposed to the modern world that they might already love God, even if they know next to nothing about Him, and do their best to be charitable, serve Him, show gratitude, and even have sorrow for their wrongdoing. One side says that if they are truly saved than God would have miraculously sent someone to baptize them, the other says that God may very well extend His salvation to such a person, but we just can't know until we have a beatific knowledge of the Mystery of Salvation Itself.
But both agree, the chances of coming across such a person is next to zero. People in general need the Gospel, that's why we are supposed to preach it and spread it. The non-Feeney-ites are not necessarily ecumenists. On the contrary. They understand very well that lies which are not the Gospel remove someone from invincible ignorance because it causes that person to be non-charitable, untrue, and anti-God. They do not doubt human nature for a moment. We are a fallen race, and need Christ and His Gospel. No Catholic (heretics who claim the name aside) disagrees on that.
Personally I am very much a non-Feeney-ite, but I am also an orthodox, Roman, Catholic Christian, or at the very least as much as I am able to be at the moment. I'm not saint obviously and work out my salvation with great fear and trembling, precisely because I am reminded of times I forget to work out my salvation at all. But I know that God is with me not because someone poured water over my head as a child, but because He loves me. The water was just an outward sign of that inward Grace, which is precisely the definition of a sacrament.