What are you referring to? I don’t think false obedience has EVER been a part of Catholic teaching…I always think it’s ironic that NeoCatholics call us protestants when we are the ones
resisting the Protestant errors in the Church today. Protestants aren’t protestants just because they disobey the Pope…they’re Protestants because they teach and believe heresies contrary to the one true Catholic faith taught from the Apostles. Only a naive, simple-minded person with a minimal grasp of Catholic teaching would think that obedience to the Pope in every single matter is the heart of Catholicism…
John Paul the Great, Paul VI, and a lot of higher-ups in the Conciliar Vatican have prayed with Protestant heretics [forbidden to Catholics until V2] and held joint worship services with them [offering false worship to God with non-catholics=a mortal sin

]…Benedict XVI even “rehabilitated” Luther, but not before His Greatness John Paul II lifted the excommunication on him [which indicates he does not believe Luther was a heretic]; heck, the preacher to the papal household, Cantalamessa, besides openly preaching other heresies contrary to the Catholic faith, has said that Luther was right and that faith alone is necessary for salvation! He preached this sermon in front of Pope Benedict XVI, but you didn’t hear a peep from anyone in the Vatican or from the NeoCatholic talking heads…but apparently if anyone preaches Catholicism as it was universally practiced and believed before Vatican II he will be censured and ultimately “excommunicated”…lol, as if a non-Catholic heretic can validly excommunicate a Catholic. Yes, it appears that the Conciliar Church is full of protestants; so I invite you now to retract your statement about Traditional Catholics.