A Catholic professes the Catholic Faith.

22. Actually only those are to be included as members of the Church who have been baptized and profess the true faith, and who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed. “For in one spirit” says the Apostle, “were we all baptized into one Body, whether Jєωs or Gentiles, whether bond or free.” ¹⁷ As therefore in the true Christian community there is only one Body, one Spirit, one Lord, and one Baptism, so there can be only one faith. ¹⁸ And therefore if a man refuse to hear the Church let him be considered — so the Lord commands — as a heathen and a publican. ¹⁹ It follows that those are divided in faith or government cannot be living in the unity of such a Body, nor can they be living the life of its one Divine Spirit.

Source: https://www.papalencyclicals.net/pius12/p12mysti.htm

The title of this thread refers to a response one might expect from an Indult or Novus Ordo attendee, when affirming to them that Vatican II heralded the establishment a new man-made religion, a Protestantised and Humanist corruption of the true Faith. From such a statement they may feel that they are being accused of not being Catholic.

How would you respond to such a rejoinder?

I am new to Tradition myself and I'm wondering what the best way of addressing the issue is to my Indult/NO friends. How can I explain that people can be Catholic while affiliated with what is not the Catholic Faith?

Correct profession doesn’t make you Catholic.  The Sacrament of Baptism, properly administered, form, matter, intent, makes a person Catholic.

There's some (tiny bit of) truth to it, but it's misused by R&R types like Father Wathen and Stubborn.

In one sense, once someone has been baptized a Catholic and come into subjection to the Pope, that relationship remains.  That's why, for instance, those who were baptized Catholic, even if raised Protestant, cannot validly marry outside the Church ... because the Church retains this jurisdiction over them.

But it's patently false to say that a Catholic can never lose membership in the Church.  There's no Pope, no Church Father, no Doctor, and no approved Catholic theologians who has ever taught that one cannot leave the Church, lose membership in the Church, and go from inside the Church to outside the Church.  That is a novelty invented by Father Wathen to explain R&R ... and Stubborn has been pushing this nonsense around here for a long time.

Now, if one wanted to argue that the Baptismal character alone suffices to hold office in the Church, even without profession of the true faith and subjection to the Holy Father, then one could try to make that case.  But "once Catholic always Catholic" is ridiculous.

Ask them what they think on EENS. That's literally the line in the sand and anyone with an ecclesiology/"ecuмenism" reconfigured by VII is in danger of not being Catholic. It's going to sound autistic but after that recent poll I think it's clearly THE defining question...

82% of "catholics" reject MULTIPLE Catholic dogmas, so I think this line of questioning is the way to go.