This is just one example to show you that the Institute and by far the vast majority of other non-SSPX orders are attached to the Tridentine Mass for a feeling of nostalgia or "preference." This is not what makes someone a Traditional Catholic.
A traditional Catholic knows that a Catholic can not attend a Novus Ordo, or go to a Novus Ordo ordained priest, or support religious liberty, ecumenism, or collegiality. Why is this? Because in so doing, they are denying the Traditional dogmas and authority of the Universal Church on ecumenism, religious liberty, and even on the propitiatory nature of the Sacrifice of the Mass. In the Novus Ordo, unlike the traditional Roman Rite (and other Traditional Rites), the word propitiatory does not appear in the beginning of the Novus Ordo Roman Missal's doctrinal exposition.
The very nature of the Novus Ordo Sacraments, while not necessary invalid (but questionable in many instances), bear in them the theology of the New Rite and the Post Vatican II Church. To frequent these Sacraments is to mix the good, true, and beautiful with that which is present in the New Sacraments: novelty. By receiving the Novus Ordo Sacraments, you profess your Communion in and with the beliefs of the Novus Ordo Church, even those beliefs that are flawed.
His Grace Bishop Williamson comments in his "Eleison Comments" #241 in February 2012 the following:
For instance a Protestant may believe in God, he may even believe in the divinity of the man Jesus of Nazareth, but if he does not believe in the Real Presence of God, body, blood, soul and divinity, beneath the appearances of bread and wine after their consecration at Mass, then he has a profoundly different and deficient concept of the love of Jesus Christ and of the God in whom he believes. Can one then say that the true Protestant and the true Catholic believe in the same God ? Vatican II says one can, and on the basis of supposedly more or less shared beliefs between Catholics and all non-Catholics, it builds its ecumenism. On the contrary Dr Schüler illustrates by a series of comparisons that what may look like the same belief, when it forms part of two different creeds, is not really the same at all. Here is one illustration: oxygen molecules mixed with nitrogen are the selfsame molecules as when compounded with hydrogen, but they are as different in the two cases as the air we breathe (O + 4N) from the water we drink (H20)!Even a number of priests offering the Traditional Sacraments (e.g. the FSSP) were ordained in the Novus Ordo ordination rite. And many priests (non SSPX that is) that happen to have received traditional ordinations, received them from bishops who were themselves ordained to the episcopacy in the Novus Ordo.
Oil and water do not mix just as theological novelties and the unerring, imputable, eternal Truths of the Catholic Faith.
Just to summarize, this particular issue is one of great complexity and no one post can do justice to the situation to explain it fully in terms of its philosophical, theological, and societal implications. I merely wish to raise the question that very few Traditionalist raise, namely, whether or not Traditional Catholics should (or can) attend the Novus Ordo.
The following segment of What We Have Lost...And the Road to Restoration helps to give a concise overview of the depths of the problem.
I would invite all of you to also read Chapter V: The Post Conciliar Church: A Question of Schism. This particular document helps go in more detail with the problems inherent in the Novus Ordo. An additional resource is the Society's page: Is the New Mass Legit?
As said by His Excellency Marcel Lefebvre, "The Novus Ordo Missae, even when said with piety and respect for the liturgical rules, is impregnated with the spirit of Protestantism...it bears within it a poison harmful to the Faith"