I had read this and I didn't do my research...so you are right...sorrrry
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https://www.pillarcatholic.com/p/is-the-sspx-pilgrimage-an-official

What has SSPX said about it?

The SSPX announced the pilgrimage in December 2024, just before the Jubilee Year officially opened.

In a letter sent to friends and benefactors, U.S. district superior Fr. John Fullerton noted that 2025 marks the 50th anniversary of a pilgrimage that SSPX founder Archbishop Marcel Lefebvre led during the 1975 Holy Year, only five years after founding the Society.

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Is it true that he celebrated the Tridentine Mass sometime somewhere at the Vatican, during his protest pilgrimage?  The link has the ENTIRE article  like a diary...

Read the article and find out! Excerpt.
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https://www.sspxasia.com/Docuмents/Archbishop-Lefebvre/Apologia/Vol_one/Chapter_6.htm

The sermon which Mgr. Lefebvre preached in the Basilica of Maxentius on 25 May 1975 was published in The Remnant of 6 March 1976. It was entitled "The One True Religion."

The One True Religion

My dear brethren:

If there is one day on which the Church's liturgy affirms our Faith, that day is the Feast of the Blessed Trinity. This morning, in the breviary which the priest formerly had to recite, he had to add to the psalms of Prime the Creed of St. Athanasius. This is the creed which affirms clearly, serenely, but perfectly, what we are bound to believe (...)Indeed, all our faith is summed up in our belief in the Most Holy Trinity and in Our Lord Jesus Christ, God made Man. The whole of our Creed, which we shall sing in a few minutes, is focused, as it were, on the very person of Our Lord Jesus Christ. He it is who is our God, He our Savior; it is through Him that we shall enter Heaven. He is the door of the sheep-fold, He is the Way, the Truth, the Life. There is no other name on earth by which we may be saved: the Gospels tell us all this.

Therefore, when our Faith is being attacked from all sides we must hold steadfastly and firmly to it. We must never accept that there can be any compromise in the affirmation of our Faith. Herein, I think, (...) this tragic situation we are going through, lies in seeing that our Faith is no longer affirmed with certainty: that through a false ecuмenism we have, as it were, reached the point of putting all religions on the same footing, of granting what is called "equal rights" to all religions. This is a tragedy because it is all entirely contrary to the truth of the Church. We believe that Our Lord Jesus Christ is our God, our Savior, our Redeemer; we believe that the Catholic Church alone has the Truth, thus we draw the proper conclusions, by respecting in our personal lives the Religion which Our Lord Jesus Christ founded. (...)

He it is who has given us the Holy Sacrifice of the Mass, He who died upon the Cross. Already on the day of the Last (...)thus making priests of those to whom He gave the power to consecrate the Eucharist. He did this by His own Will, His Will as God, because Jesus Christ is God; He has, thus, given us the Holy Sacrifice of the Mass, which we love so much, which is our life, our hope, and our salvation. This Sacrifice of Calvary cannot be transformed, the Sacrifice of the Last Supper cannot be transformed - for there was a Sacrifice at the Last Supper - we cannot transform this Sacrifice into a simple commemorative meal, a simple repast at which a memory is recalled, this is not possible. To do such a thing would be to destroy the whole of our Religion, to destroy the most precious thing which Our Lord has given us here on earth, the immaculate( ...)
The Church is essentially priestly because she offers the redemptive Sacrifice which Our Lord made on Calvary, and which she renews upon our altars. For a true Catholic, one who is truly faithful to Our Lord Jesus Christ, anything which touches what He Himself established moves him to the very depths of his heart, for he loves it as the apple of his eye. So, if it comes, in any way, to the point of destroying from within what Our Lord Jesus Christ gave to us as the source of life, as the source of grace, then we suffer, we suffer dreadfully, and we demand absolutely that this spring, this fountain of life, this fountain of eternal life, this fountain of Grace be preserved for us whole and entire.

And if such is true of the Holy Sacrifice of the Mass, it is also true of the Sacraments. It is not possible to make any considerable changes in the Sacraments without destroying them, without running the risk of rendering them invalid, and consequently without running the risk of drying up the grace, the supernatural and eternal life which they bring to us. It is again Our Lord Jesus Christ Himself who established the Sacraments; it is not for us, we are not the masters of the Sacraments: even the Sovereign Pontiff cannot change them. Without doubt he can make changes in the rites, in what is accidental in any Sacrament; but no Sovereign Pontiff can change the substance of a Sacrament, for that was established by Our Lord Jesus Christ. It is Our Lord Jesus Christ Himself who took such care in the founding of our holy Religion, Who left us directions as to what we must do, Who gave Himself to us in the Holy Eucharist through the Holy Sacrifice of the Mass. What more could we ask? What other religion can lay claim to possess such a thing? And why? Because the only true religion is that of the Catholic Church.

This is a matter of fundamental importance, fundamental for our behavior, fundamental for our religion, and fundamental also for the way we should behave towards those people who do not believe in our holy Religion. This is extremely important, because it is precisely towards those who do not believe, those who do not have our Faith, that we must have immense charity, the true charity. We must not deceive them by telling them that their religion is as good as ours - that is a lie, that is selfishness, that is not true charity. If we consider what profound riches have been given to us in this Religion of ours, then we should have the desire to make it known to others, and share these riches and not say to them: "But you already have all you need! There is no point in your joining us, your religion is as good as ours." See how this matter is one of paramount importance, for it is precisely such false ecuмenism which makes the adherents of all the other religions believe that they have certain means of salvation. Now this is false. Only the Catholic Religion, and only the Mystical Body of Christ, possesses the means of salvation. We cannot be saved without Jesus, and we cannot be saved without grace. "He who does not believe," said Our Lord, "will be condemned." We must believe in Our Lord Jesus Christ in order to be saved. "He who believes shall be saved; he who obeys My commandments shall have eternal life; he who eats My Flesh and drinks My Blood shall have eternal life." Here is what Our Lord taught us. Therefore, we should have a tremendous desire, a really tremendous desire, to communicate our Faith to others. And this is exactly what made the missionary spirit of the Church. If the strength, the certainty, of our faith is weakened, then the missionary spirit of the Church also diminishes, since it is no longer necessary to cross the seas, to cross the oceans, to go and preach the Gospel, for what is the good of it? Let us leave each man to his own religion, if that religion is going to save him.

Therefore, we must hold fast to our Faith, we must adhere strictly to its affirmation, and we must not accept this false ecuмenism which makes all religions into sister-religions of Christianity, for they are nothing of the kind. It is very important to state this nowadays, because it is precisely this false ecuмenism which had too much influence after the Council. False ecuмenism is the reason why the seminaries are empty. Why is this so? Why are there no more vocations for the missionary orders? Precisely because young men no longer feel the need to make the Truth known to the whole world. They no longer feel the need to give themselves completely to Our Lord Jesus Christ simply because Our Lord Jesus Christ is the only Truth, the only Way, the only Life. What attracts the young to preach the Gospel is that they know they have the Truth. If vocations are withering away, it is due to this false ecuмenism. How we suffer at the thought that, in certain countries, people speak of "eucharistic hospitality," of "inter-communion" - as if one could give the Body and Blood of Our Lord Jesus Christ to those who do not believe in the Body and Blood of Our Lord Jesus Christ, consequently to those who do not adore the Holy Eucharist, because they do not believe in it! Without sacrilege, without blasphemy, the Body and Blood of Our Savior cannot be given to a person who denies His Real Presence in the Eucharist. On this point, therefore, we must have a firm and solid faith, a faith which does not compromise. This is entirely in keeping with the tradition of the Church.

Thus the martyrs believed who lie buried everywhere in this basilica, and in all the churches of Rome, who suffered here in this forum of Augustus, who lived among pagans for three centuries and were persecuted as soon as they were known to be Christians. They were thrown into prison...our thoughts turn to the Mamertine prison, so close to us here, where Peter and Paul were put in chains because of their faith: And shall we be afraid to affirm our faith? We would not in that case be the true descendants of the martyrs, the true descendants of those Christians who shed their blood for Our Lord Jesus Christ in affirmation of their faith in Him. They, too, could indeed have said, "But, since all religions are of equal value, if I burn a little incense before an idol, what does that matter? My life will be saved." But they preferred to die, they preferred to be thrown to the beasts in the Colosseum, quite close to us here. So many, many martyrs were thrown to the beasts, rather than offer incense to pagan gods!

So, may our presence here in Rome be an occasion for us to strengthen our faith, to have, if necessary, the souls of martyrs, the souls of witnesses (for a martyr is a witness), the souls of witnesses of Our Lord Jesus Christ, witnesses of the Church. Here is what I wish you, my most dear brethren, and in this we must be unflinching, whatever happens. We must never agree to diminish our faith; and if by misfortune it were to happen that those who ought to defend our Faith came to tell us to lessen or diminish it, then we must say: "NO." Saint Paul put this very well: "Though we, or an angel from heaven, preach a gospel to you besides that which we have preached to you, let him be anathema." Well, that, I think, sums up clearly what I wanted to say to you, so that when you return to your homes you may have the courage, the strength, despite difficulties, despite trials, to remain true to your Faith, come what may,  We must think on these things, (...)  because it is what Our Lord told us: "If we do not believe, we shall be condemned."

Well, I’d unboggle my mind and forget about what other people do or what they call themselves. They are not your responsibility. People do as they please. In this case, don’t sweat it.