This is an interesting thread. I have to answer the question by using my story, because it’s easier to answer from my lived experience than from concepts.
I’m a Traditional Catholic.
What does that mean?
I’m faithful to the Church and to the papacy from Peter to Francis. I accept that the Holy Father has the authority to govern the Church and to make prudential decisions and that his power and authority are not limited to faith and morals; therefore, our obedience is not limited to faith and morals, but to all legitimate governance.
I’m faithful to the life of prayer that I’ve inherited from Catholic Spirituality and to the sacramental life of the Church, regardless of its external form. The Sacraments in any form, as long as they are valid and legal, remain our surest font of grace.
I also understand that the tradition of the Church is very broad. Within that tradition there are smaller traditions, for example my Franciscan tradition.
Therefore, as a Franciscan, I embrace material poverty and identify with those who are materially poor by living among them, serving them and seeing Christ in them as well as taking Christ to them. I submit to the wishes of my bishop and my pope as was the mind of my Holy Father Francis. I also submit to the authority of the general chapter of my community as has been our tradition since Francis started general chapters in 1223. And I understand that I have no right to feelings or opinions of my own that are in conflict with Francis, my superiors, my bishop or my pope, except in matters of sin. This is the perfection of poverty and charity.
As superior, I try to govern as Francis commands, to be a mother to my brothers by nurturing them, encouraging them, correcting them, protecting them, and forming them to live in the Church and the greater world beyond the institutional Church.
I subscribe to the idea the Holy Sacrifice of the mass, in all its forms, is sacred. The forms are different, but each has layers of richness that God has allowed for our good. It is up to us to open our eyes and search through those layers. I’m not tied to any form of the mass in the Roman Rite, or any rite in the Universal Church, because they’re all part of our Catholic tradition. I understand that there are points of conception where certain traditions are born and if we are faithful to the intent of the Church and carry them forward as the Church envisions them, eventually, they will become woven into the fabric of ecclesial life and tradition.
I subscribe to everything that the Church teaches on matters of faith and morals and at the same time, like my father, St. Francis, I believe that there are times when we must revise how we say things depending of our audience and cultural context. So in this sense, even the revision of the delivery is traditional, because this concept and permission was granted to us by our founder 800 years ago.
In my personal life, I have in my possession two habits, one pair of pants and one pair of jeans, three sets of underwear, no medical insurance, not retirement plan, no house of my own nor owned by our community. We live in borrowed houses or rented houses. This is part of Franciscan tradition, which the Church has blessed, because she believes that it leads to salvation. The Church does not approve of any way of life that is not conducive to the perfection of charity and the salvation of the soul.
We keep our liturgy dignified but simple as did Francis and Clare. The focus is on the three points of our Franciscan tradition: Christ’s sacrifice, the Word, and the brothers gathered to offer the sacrifice served by one of our own who presides through his priestly ministry. But he presides, not as one who is above, but as a brother who is called to the priesthood of Jesus Christ so that he may serve his brothers.
Like our early Franciscans and our brothers through the centuries, I believe that every man and woman, regardless of creed is a brother and sisters redeemed by Christ. Regardless of their relationship with God, they are in a much better situation than I am, because to whom much is given, of him much is required. And I acknowledge that I have received the fullness of faith, but have not given back proportionately. So I can only serve those people with great humility and docility, inviting them to know Christ and to walk the road of penance and conversion with me, not pushing them, because I have betrayed him. They have not, because they do not know him as I have come to know him.
Finally, I’m a son of the Immaculate and I depend on her prayers and her guidance to do what her son tells me.