Whoa! You have been given a lot of misinformation here. Let’s back peddle. SSPX and FSSP are secular, not religious. Religious are consecrated men or women who make vows in a stable community canonically erected by either the Pope or the local bishop.
There are four kinds of religious institutes: congregations, orders, societies and abbeys. The Opus Dei, SSPX and FSSP do not belong to any of these. They are secular men who are ordained priests, but they remain in the secular state, because they do not make vows. The FSSP and SSPX are Secular Clerical Societies of Apostolic Life. The Opus Dei is a Personal Prelature of the Holy Father. It is not an order, congregation, society, or an institute. Within the Prelature, there are Public Associations of the Faithful. The Opus Dei are big defenders of tradition, but they celebrate only the OF. They are not allowed to celebrate the EF without permission of the Holy Father himself. He is their Superior General. Currently, they have a vicar appointed to govern them in the name of the Holy Father.
Currently, there are no religious orders in the Catholic Church that celebrate the EF. There are some religious orders that have their own rite, which is in Latin and very similar to the EF, but it’s not the Tridentine form. The Tridentine form is part of the Roman Rite. These other rites are not part of the Roman Rite, though they are Latin Rites: ie. Carthusian Rite.
There are some religious congregations that celebrate the EF: Sons of the Most Holy Redeemer, Franciscans of the Immaculate, Franciscans of the Eternal Word and others. The Franciscans use both the EF and the OF. The Major Superiors of the Franciscans have never given permission for exclusive use of the EF. However, the Franciscans of the Immaculate are often given the permission by houses, if they can guarantee that they will not refuse to celebrate the OF when asked to do so by the brotherhood.
There are also religious societies that celebrate the EF: Canons of St. John Cantius come to mind right away. There are a few others.
In the Catholic Churches (all 22 of them) there is only one order of priests, the Jesuits. Religious orders of men are broken down into the following: hermits, monks, friars and clerks regular. In these orders a man may be a priest, if he is approved by his superior and by his brothers. He cannot choose to be a priest without permission. The order can deny the permission for ordination, but he remains a member of the order until death. The vows supersede the Sacrament of Holy Orders. You may not ask for Holy Orders until you have made solemn vows until death. By that time, if you are denied permission to be ordained, it’s too late to leave. Only the Holy Father can dispense you from the vows. You will recognize the orders because we have the letter “O” after our name. For example, my initials are OSF (Order of St. Francis). An Augustinian is OSA. The Jesuits are the only order that I know that is referred to as a society, but is really an order. They are Clerks Regular.
The Dominicans, Augustinians, Carthusians, Cistercians and Carmelites are what we call clerical institutes. They are orders of friars or monks, but the clerics are the only ones allowed to govern. That is the only difference between an ordained brother and a non-cleric brother.
We do have religious congregations of priests. Religious congregations are not orders. They make vows, live in community, but do not have the same rights as the orders or the same spiritual benefits. Their way of life is very different from the orders.
I hope this helped.
Fraternally,
Br. JR, OSF
