I saw the thread about the SSPX. I tend to combine these two branches. Can anyone tell me the difference? I think the FSSP is in communion with Rome, but I am not sure. Why are they so controversial? Why do they seem to be outside the mainstream of Catholicism? Or are they? I liked it better when we were “One, holy, catholic and apostolic” !!
FSSP is very much Catholic and in communion with Rome.
They are not controversial at all, as far as I know. Do not confuse them with SSPX or SSPV.
The FSSP is completely in union with Rome. They were founded in 1988 by Bl. John Paul II.
It’s founding was led by a group of priests from the SSPX who no longer wanted association with that group due to disobedience.
This is a quote from their declaration in 1988.
“For the honour and glory of the holy Catholic Church, for the consolation of the much troubled faithful, and for the peace of their conscience, the undersigned, members until now of the Fraternity of Saint Pius X, declare with profound regret over the illicit consecration of bishops on 30 June  that they have remained within the Catholic Church as pars sanior of this same Fraternity, and that they have but one desire: to be able to live as a religious society in this Church and place themselves at her service under the authority, of course, of the Roman Pontiff, her supreme head.”
Question correctly answered.