Let's all please calm down and discuss this rationally, there's no need for polemics.
Fr. Kramer, if you want 20th and 19th century theologians who hold and defend the teaching in question, I will give you two of the highest repute - Fr. Michael Mueller, CSSR, who singlehandedly oversaw innumerable conversions into the Church, (and good friend of Fr. Arnold Damen, who himself personally received 13,000 heretics into the Church), and who never published anything withtout the approval of two of his superiors, and Msgr. Fenton, who needs no introduction.
1. Fr. Michael Mueller at the turn of the 19th century cites many authorities in its favor,
This doctrine is clearly expressed in the following words of the Athanasian Creed: "He, therefore, who wishes to be saved, must thus think of the Trinity," that is, he must believe the doctrine of the Holy Trinity as explained in this Creed. "Furthermore it is necessary to everlasting salvation that he also believe rightly the Incarnation of our Lord Jesus Christ. Hence St. Peter says: "Be it known to you, that there is no salvation in any other name than that of Jesus Christ; for there is no other name under heaven given to men whereby we must be saved." (Acts, iv. 10, 10).
"Thus," says St. Alphonsus, " there is no hope of salvation except in the merits of Jesus Christ. Hence St. Thomas and all theologians conclude that, since the promulgation of the Gospel, it is necessary, not only as a matter of precept, but also as a means of salvation (necessitate medii, without which no adult can be saved), to believe explicitly that we can be saved only through our Redeemer." (Reflections on the Passion of Jesus Christ, Chapt. I., No. 19).
The explicit belief in the mysteries of the Holy Trinity and of the Incarnation of the Son of God is therefore of the greatest importance. This belief teaches the origin of the world, its creation by God the Father; it teaches us the supernatural end of man, his fall, and the redemption of mankind by God the Son; it teaches the sanctification of souls by the gifts of the Holy Ghost ...
Likewise, Fr. Fenton in the 1950s tells us,
... most theologians teach that the minimum explicit content of supernatural and salvific faith includes, not only the truths of God’s existence and of His action as the Rewarder of good and the Punisher of evil, but also the mysteries of the Blessed Trinity and the Incarnation.
Each of these theologians, like St. Alphonsus and others, cite many authorities in their works, and strenuously argue in favor of this teaching, which it is certainly their right and, as I will show below, arguably their duty, to do.
2. From the Popes,
"A great number of those who are condemned to eternal punishment suffer that everlasting calamity because of ignorance of those mysteries of Faith which must be known and believed in order to be numbered among the elect."
What is a mystery of Faith? A mystery of Faith is a truth to which natural reason cannot attain, it is the proper object of supernatural Faith, according to Vatican I.
With regard to the source, we know at the one level by natural reason, at the other level by divine faith. With regard to the object, besides those things to which natural reason can attain, there are proposed for our belief mysteries hidden in God which, unless they are divinely revealed, are incapable of being known.
There is a much earlier Holy Office decree, which was promulgated in the context of a missionary asking whether someone could be baptized with a promise to believe, but without actually believing the Faith. Rome's answer was that as the primary mysteries of the Faith like the Trinity and Incarnation are necessary as a means, therefore, a promise is not sufficient, but these must be explicitly confessed by all adults, even dying ones.
A promise is not sufficient, but a missionary is bound to explain to an adult, even a dying one who is not entirely incapacitated, the mysteries of Faith which are necessary by a necessity of means, as are especially the mysteries of the Trinity and the Incarnation.”
Now, it doesn't seem that this can be reconciled with your opinion. If you wish to argue to the contrary, then give some explanation for these statements. In that St. Pius X in particular says "known", he rules out a mere implicit belief in these mysteries, and says it must be explicitly believed, or known.
3. Fr. Kramer, you have yourself said you think Fr. Feeney was a good man, and I agree. Fr. Feeney did not know how to answer those who were saying Jews and Protestants can be saved without being Catholic, and so do not need to convert. So, he mad the mistake that he did. But let's leave Fr. Feeney for a moment. Today, over a billion nominal Catholics, and the leaders of the mainstream Church, no longer believe the Catholic Faith is a means without which salvation cannot be attained, they no longer tell Jews and Protestants, or anyone else for that matter, that they must be Catholic to be saved. Do you deny that false ecuмenism and interfaith horrors would not be possible if they did?
Also, how can we credibly claim to be traditional Catholics if we positively refuse to believe something upheld by very great traditional authorities?
This is consecrated Tradition, it is taught by the Church, Her Popes, Saints, Doctors, Fathers. It is taught by St. Thomas and St. Alphonsus, St. Bernard and St. Robert, St. Augustine and St. Ambrose. It is contained in the Athanasian Creed, which is infallible, and taught by Popes down to Gregory XVI, Pius IX and St. Pius X, and, if you desire to hear it from them, other traditional Catholic theologians like Fr. Mueller and Msgr. Fenton before Vatican II.